Relevant bibliographies by topics / Numerical error / Dissertations / Theses
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Dissertations / Theses on the topic 'Numerical error'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 December 2024

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1

Jenkins, Siân. "Numerical model error in data assimilation." Thesis, University of Bath, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665395.

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In this thesis, we produce a rigorous and quantitative analysis of the errors introduced by finite difference schemes into strong constraint 4D-Variational (4D-Var) data assimilation. Strong constraint 4D-Var data assimilation is a method that solves a particular kind of inverse problem; given a set of observations and a numerical model for a physical system together with a priori information on the initial condition, estimate an improved initial condition for the numerical model, known as the analysis vector. This method has many forms of error affecting the accuracy of the analysis vector, a
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2

Reddinger, Kaitlin Sue. "Numerical Stability & Numerical Smoothness of Ordinary Differential Equations." Bowling Green State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1431597407.

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3

Tomita, Yu. "Numerical and analytical studies of quantum error correction." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53468.

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A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computa
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4

Romutis, Todd. "Numerical Smoothness and Error Analysis for Parabolic Equations." Bowling Green State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1522150799203255.

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5

Harlim, John. "Errors in the initial conditions for numerical weather prediction a study of error growth patterns and error reduction with ensemble filtering /." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3430.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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6

Pinchuk, Amy Ruth. "Automatic adaptive finite element mesh generation and error estimation." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63269.

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7

Küther, Marc. "Error estimates for numerical approximations to scalar conservation laws." [S.l. : s.n.], 2001. http://www.freidok.uni-freiburg.de/volltexte/337.

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8

Ndamase-, Nzuzo Pumla Patricia. "Numerical error analysis in foundation phase (Grade 3) mathematics." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/5893.

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The focus of the research was on numerical errors committed in foundation phase mathematics. It therefore explored: (1) numerical errors learners in foundation phase mathematics encounter (2) relationships underlying numerical errors and (3) the implementable strategies suitable for understanding numerical error analysis in foundation phase mathematics (Grade 3). From 375 learners who formed the population of the study in the primary schools (16 in total), the researcher selected by means of a simple random sample technique 80 learners as the sample size, which constituted 10% of the populatio
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9

Higham, D. J. "Error control in nonstiff initial value solvers." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234210.

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10

Wyant, Timothy Joseph. "Numerical study of error propagation in Monte Carlo depletion simulations." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44809.

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Improving computer technology and the desire to more accurately model the heterogeneity of the nuclear reactor environment have made the use of Monte Carlo depletion codes more attractive in recent years, and feasible (if not practical) even for 3-D depletion simulation. However, in this case statistical uncertainty is combined with error propagating through the calculation from previous steps. In an effort to understand this error propagation, four test problems were developed to test error propagation in the fuel assembly and core domains. Three test cases modeled and tracked individual
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11

Lawson, Jane. "Towards error control for the numerical solution of parabolic equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329947.

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12

Maclean, John. "Numerical multiscale methods for ordinary differential equations." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12818.

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This thesis is concerned with a class of explicit numerical methods for multiscale differential equations, including the Heterogeneous Multiscale Methods (HMM) and Projective Integration (PI) methods. These techniques have been developed within the last decade and successfully applied to a wide range of multiscale problems. We examine the HMM and PI methods when applied to multiscale systems for which the dynamics converges rapidly to a lower dimensional manifold defined in terms of the slow degrees of freedom, and provide rigorous convergence results for the methods under these conditions. Th
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13

Balsubramanian, Ravishankar. "Error estimation and grid adaptation for functional outputs using discrete-adjoint sensitivity analysis." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-10032002-113749.

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14

Tyson, William Conrad. "On Numerical Error Estimation for the Finite-Volume Method with an Application to Computational Fluid Dynamics." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/86193.

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Computational fluid dynamics (CFD) simulations can provide tremendous insight into complex physical processes and are often faster and more cost-effective to execute than experiments. However, each CFD result inherently contains numerical errors that can significantly degrade the accuracy of a simulation. Discretization error is typically the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since the generation, transport, and diffusion of these errors is a highly nonlinear function of the computational grid and di
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15

Camacho, Fernando F. "A Posteriori Error Estimates for Surface Finite Element Methods." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/21.

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Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases. In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for
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16

Thakre, Purva. "USING A NUMERICAL ALGORITHM TO SEARCH FOR DECOHERENCE-FREE SUB-SYSTEMS." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/theses/2465.

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In this paper, we discuss the need for quantum error correction. We also describe some basic techniques used in quantum error correction which includes decoherence-free subspaces and subsystems. These subspaces and subsystems are described in detail. We also introduce a numerical algorithm that was used previously to search for these decoherence-free subspaces and subsystems under collective error. It is useful to search for them as they can be used to store quantum information. We use this algorithm in some specific examples involving qubits and qutrits. The results of these algorithm are the
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17

Kuhn, Wolfgang. "Rigorous and reasonable error bounds for the numerical solution of dynamical systems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28941.

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18

Hu, Lili. "Numerical algorithms based on the back and forth error compensation and correction." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/54839.

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In this thesis we carry out a further study of the back and forth error compensation and correction (BFECC) method. The first part discusses the time reversibility of numerical schemes. Motivated by the BFECC method, a variety of new numeri- cal schemes that aim at improving the time reversibility are developed and studied. We also introduce an interpolation algorithm based on BFECC in this part. In the second part we introduce a new limiting strategy which requires another backward advection in time so that overshoots/undershoots at the new time level get exposed when they are transformed bac
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19

Tenwick, Michelle Claire. "Error estimates for numerical solutions of one- and two-dimensional integral equations." Thesis, University of Leeds, 2012. http://etheses.whiterose.ac.uk/3405/.

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This thesis is concerned with the improvement of numerical methods, specifically boundaryelement methods (BEMs), for solving Fredholm integral equations in both one- and two dimensions. The improvements are based on novel (computer-algebra-based) error analyses that yield explicit forms of correction terms for a priori incorporation into BEM methods employing piecewise-polynomial interpolation in the numerical approximation. The work is motivated by the aim of reducing errors of BEM methods for low-degree interpolating polynomials, without significantly increasing the computational cost associ
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20

Shaw, Jeremy A. "Computational Algorithms for Improved Representation of the Model Error Covariance in Weak-Constraint 4D-Var." PDXScholar, 2017. https://pdxscholar.library.pdx.edu/open_access_etds/3473.

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Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error c
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21

Shahabi, Majid. "The distribution of the classical error terms of prime number theory." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012, 2012. http://hdl.handle.net/10133/3252.

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22

Raju, Anil Roy Christopher J. "Discretization error estimation using the method of nearby problems one-dimensional cases/." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Thesis/RAJU_ANIL_41.pdf.

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23

Nešpor, Vladislav. "Investigation of wind-induced error of precipitation measurements using a three-dimensional numerical simulation /." Zürich, 1995. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=11060.

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24

Czuprynski, Kenneth Daniel. "Numerical analysis in energy dependent radiative transfer." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5925.

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The radiative transfer equation (RTE) models the transport of radiation through a participating medium. In particular, it captures how radiation is scattered, emitted, and absorbed as it interacts with the medium. This process arises in numerous application areas, including: neutron transport in nuclear reactors, radiation therapy in cancer treatment planning, and the investigation of forming galaxies in astrophysics. As a result, there is great interest in the solution of the RTE in many different fields. We consider the energy dependent form of the RTE and allow media containing regions of n
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25

Wu, Jian. "Numerical Smoothness of ENO and WENO Schemes for Nonlinear Conservation Laws." Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1307575652.

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26

Warner, Michael S. "Numerical solutions to optimal-control problems by finite elements in time with adaptive error control." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/11844.

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27

Kalaver, Satchidanand Anil. "Management of reference frames in simulation and its application to error reduction in numerical integration." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/12406.

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28

Matthews, Charles. "Error in the invariant measure of numerical discretization schemes for canonical sampling of molecular dynamics." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8949.

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Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many appl
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29

Kadir, Ashraful. "Numerical Methods for Molecular Dynamics with Nearly Crossing Potential Surfaces." Doctoral thesis, KTH, Matematik (Inst.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-195098.

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This thesis consists of four papers that concern error estimates for the Born-Oppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics. In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of observables for the time-independent Schrödinger equation, with matrix valued potentials, and the values of observables for the ab initio Born-Oppenheimer molecular dynamics of the ground state depends
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30

Hoel, Håkon. "Complexity and Error Analysis of Numerical Methods for Wireless Channels, SDE, Random Variables and Quantum Mechanics." Doctoral thesis, KTH, Numerisk analys, NA (stängd 2012-06-30), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-94150.

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This thesis consists of the four papers which consider different aspects of stochastic process modeling, error analysis, and minimization of computational cost.      In Paper I, we construct a Multipath Fading Channel (MFC) model for wireless channels with noise introduced through scatterers flipping on and off. By coarse graining the MFC model a Gaussian process channel model is developed. Complexity and accuracy comparisons of the models are conducted.      In Paper II, we generalize a multilevel Forward Euler Monte Carlo method introduced by Mike Giles for the approximation of expected valu
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31

Moan, Per Christian. "On backward error analysis and Nekhoroshev stability in the numerical analysis of conservative systems of ODEs." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620431.

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32

Murali, Vasanth Kumar. "Code verification using the method of manufactured solutions." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-11112002-121649.

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33

Evans, M. E. "Numerical analysis of error sources associated with a laser interferometer used in the calibration of rotary tables." Thesis, Swansea University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636933.

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The main objective of the work was to investigate the measurement errors in an interferometer system which arise from manufacture or from the level of skill of the operator. A computer model using a ray-trace was used to simulate the use of the interferometer in calibrating a rotary table. This application of an angle measuring interferometer is currently being developed by Renishaw Transducer Systems, Ltd. as an extension to their existing product. The errors associated with this application have been investigated both in isolation and in combination. The theoretical results indicate that wit
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34

Bondarava, Alina Verfasser], and Klaus [Akademischer Betreuer] [Deckelnick. "Stability and error analysis for a numerical scheme to approximate elastic flow / Alina Bondarava. Betreuer: Klaus Deckelnick." Magdeburg : Universitätsbibliothek, 2015. http://d-nb.info/1082625825/34.

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35

Veluri, Subrahmanya Pavan Kumar. "Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28715.

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A detailed code verification study of an unstructured finite volume Computational Fluid Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to generate exact solutions for the Euler and Navier-Stokes equations to verify the correctness of the code through order of accuracy testing. The verification testing is performed on different mesh types which include triangular and quadrilateral elements in 2D and tetrahedral, prismatic, and hexahedral elements in 3D. The requirements of systematic mesh refinement are discussed, particularly in regards to unstructured meshes. D
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36

Lux, Thomas Christian Hansen. "Interpolants, Error Bounds, and Mathematical Software for Modeling and Predicting Variability in Computer Systems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/100059.

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Function approximation is an important problem. This work presents applications of interpolants to modeling random variables. Specifically, this work studies the prediction of distributions of random variables applied to computer system throughput variability. Existing approximation methods including multivariate adaptive regression splines, support vector regressors, multilayer perceptrons, Shepard variants, and the Delaunay mesh are investigated in the context of computer variability modeling. New methods of approximation using Box splines, Voronoi cells, and Delaunay for interpolating distr
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37

Kalaver, Satchidanand Anil. "Management of Reference Frames in Simulation and its Applications." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10492.

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The choice of reference frames used in simulations is typically fixed in dynamic models based on modeling decisions made early during their development, restricting model fidelity, numerical accuracy and integration into large-scale simulations. Individual simulation components typically need to model the transformations between multiple reference frames in order to interact with other components, resulting in additional development effort, time and cost. This dissertation describes the methods for defining and managing different reference frames in a simulation, thereby creating a shared sim
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38

Asner, Liya. "Efficient numerical methods for the solution of coupled multiphysics problems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a38b0c37-f18e-4c05-adbb-b57c911feeb9.

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Multiphysics systems with interface coupling are used to model a variety of physical phenomena, such as arterial blood flow, air flow around aeroplane wings, or interactions between surface and ground water flows. Numerical methods enable the practical application of these models through computer simulations. Specifically a high level of detail and accuracy is achieved in finite element methods by discretisations which use extremely large numbers of degrees of freedom, rendering the solution process challenging from the computational perspective. In this thesis we address this challenge by dev
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39

Pong, Tak-Yun G. "Use of microcomputers in mathematics in Hong Kong higher education." Thesis, Loughborough University, 1988. https://dspace.lboro.ac.uk/2134/19483.

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Since the innovation of computers some 40 years ago and the introduction of microcomputers in 1975, computers are playing an active role in education processes and altering the pattern of interaction between teacher and student in the classroom. Computer assisted learning has been seen as a revolution in education. In this research, the author has studied the impact of using microcomputers on mathematical education, particularly at the Hong Kong tertiary level, in different perspectives. Two computer software packages have been developed on the microcomputer. The consideration of the topic to
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40

Zavar, Moosavi Azam Sadat. "Probabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantification." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82491.

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Simulations and modeling of large-scale systems are vital to understanding real world phenomena. However, even advanced numerical models can only approximate the true physics. The discrepancy between model results and nature can be attributed to different sources of uncertainty including the parameters of the model, input data, or some missing physics that is not included in the model due to a lack of knowledge or high computational costs. Uncertainty reduction approaches seek to improve the model accuracy by decreasing the overall uncertainties in models. Aiming to contribute to this area,
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41

Ortner, Christoph. "Analysis of the quasicontinuum method." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:664de544-d57d-4bca-9c5d-558f4c4e93f4.

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The aim of this work is to provide a mathematical and numerical analysis of the static quasicontinuum (QC) method. The QC method is, in essence, a finite element method for atomistic material models. By restricting the set of admissible deformations to linear splines with respect to a finite element mesh, the computational complexity of atomistic material models is reduced considerably. We begin with a general review of atomistic material models and the QC method and, most importantly, a thorough discussion of the correct concept of static equilibrium. For example, it is shown that, in contras
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42

Fischer, Manfred M., and Petra Staufer-Steinnocher. "Optimization in an Error Backpropagation Neural Network Environment with a Performance Test on a Pattern Classification Problem." WU Vienna University of Economics and Business, 1998. http://epub.wu.ac.at/4150/1/WSG_DP_6298.pdf.

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Various techniques of optimizing the multiple class cross-entropy error function to train single hidden layer neural network classifiers with softmax output transfer functions are investigated on a real-world multispectral pixel-by-pixel classification problem that is of fundamental importance in remote sensing. These techniques include epoch-based and batch versions of backpropagation of gradient descent, PR-conjugate gradient and BFGS quasi-Newton errors. The method of choice depends upon the nature of the learning task and whether one wants to optimize learning for speed or generaliz
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43

Volmer, Julia Louisa. "New attempts for error reduction in lattice field theory calculations." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19350.

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Gitter QCD ist ein erfolgreiches Instrument zur nicht-perturbativen Berechnung von QCD Observablen. Die hierfür notwendige Auswertung des QCD Pfadintegrals besteht aus zwei Teilen: Zuerst werden Stützstellen generiert, an denen danach das Pfadintegral ausgewertet wird. In der Regel werden für den ersten Teil Markov-chain Monte Carlo (MCMC) Methoden verwendet, die für die meisten Anwendungen sehr gute Ergebnisse liefern, aber auch Probleme wie eine langsame Fehlerskalierung und das numerische Vorzeichenproblem bergen. Der zweite Teil beinhaltet die Berechnung von Quark zusammenhängenden und unz
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44

Gonçalves, João Luis 1982. "Indicadores de erros a posteriori na aproximação de funcionais de soluções de problemas elípticos no contexto do método Galerkin descontínuo hp-adaptivo." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306590.

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Orientador: Sônia Maria Gomes, Philippe Remy Bernard Devloo, Igor Mozolevski<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-19T03:23:02Z (GMT). No. of bitstreams: 1 Goncalves_JoaoLuis_D.pdf: 15054031 bytes, checksum: 23ef9ef75ca5a7ae7455135fc552a678 (MD5) Previous issue date: 2011<br>Resumo: Neste trabalho, estudamos indicadores a posteriori para o erro na aproximação de funcionais das soluções das equações biharmônica e de Poisson obtidas pelo método de Galerkin descontínuo. A metod
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45

Plet, Antoine. "Contribution to error analysis of algorithms in floating-point arithmetic." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN038/document.

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L’arithmétique virgule flottante est une approximation de l’arithmétique réelle dans laquelle chaque opération peut introduire une erreur. La norme IEEE 754 requiert que les opérations élémentaires soient aussi précises que possible, mais au cours d’un calcul, les erreurs d’arrondi s’accumulent et peuvent conduire à des résultats totalement faussés. Cela arrive avec une expression aussi simple que ab + cd, pour laquelle l’algorithme naïf retourne parfois un résultat aberrant, avec une erreur relative largement supérieure à 1. Il est donc important d’analyser les algorithmes utilisés pour contr
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Davis, Clayton Paul. "Understanding and Improving Moment Method Scattering Solutions." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd620.pdf.

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47

Mautner, Karin. "Numerical treatment of the Black-Scholes variational inequality in computational finance." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2007. http://dx.doi.org/10.18452/15595.

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In der Finanzmathematik hat der Besitzer einer amerikanische Option das Recht aber nicht die Pflicht, eine Aktie innerhalb eines bestimmten Zeitraums, für einen bestimmten Preis zu kaufen oder zu verkaufen. Die Bewertung einer amerikanische Option wird als so genanntes optimale stopping Problem formuliert. Erfolgt die Modellierung des Aktienkurses durch eine geometrische Brownsche Bewegung, wird der Wert einer amerikanischen Option durch ein deterministisches freies Randwertproblem (FRWP), oder einer äquivalenten Variationsungleichung (VU) auf ganz R in gewichteten Sobolev Räumen gegebe
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48

Rana, Muhammad Sohel. "Analysis and Implementation of Numerical Methods for Solving Ordinary Differential Equations." TopSCHOLAR®, 2017. https://digitalcommons.wku.edu/theses/2053.

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Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number
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Nilsson, Martin. "Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3884.

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Cibik, Aytekin Bayram. "Numerical Analysis Of A Projection-based Stabilization Method For The Natural Convection Problems." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613465/index.pdf.

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In this thesis, we consider a projection-based stabilization method for solving buoyancy driven flows (natural convection problems). The method consists of adding global stabilization for all scales and then anti-diffusing these effects on the large scales defined by projections into appropriate function spaces. In this way, stabilization acts only on the small scales. We consider two different variations of buoyancy driven flows based on the projection-based stabilization. First, we focus on the steady-state natural convection problem of heat transport through combined solid and fluid media i
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