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Dissertations / Theses on the topic 'A posteriori error bound'

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Published: 6 September 2023

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1

Kunert, Gerd, Zoubida Mghazli, and Serge Nicaise. "A posteriori error estimation for a finite volume discretization on anisotropic meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601352.

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A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust wi

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2

Rankin, Richard Andrew Robert. "Fully computable a posteriori error bounds for noncomforming and discontinuous galekin finite elemant approximation." Thesis, University of Strathclyde, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501776.

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We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm of the error in nonconforming and discontinuous Galerkin finite element approximations of a linear second ore elliptic problem on meshes omprised of triangular elements. We do this for nonconforming finite element approximations of uniform arbitrary order as well as for non-uniform order symmetric interior penalty Galerkin, non-symmetric interior penalty Galerkin and ncomplete interior penalty Galerkin finite element approximations.

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3

Merdon, Christian. "Aspects of guaranteed error control in computations for partial differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16818.

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Diese Arbeit behandelt garantierte Fehlerkontrolle für elliptische partielle Differentialgleichungen anhand des Poisson-Modellproblems, des Stokes-Problems und des Hindernisproblems. Hierzu werden garantierte obere Schranken für den Energiefehler zwischen exakter Lösung und diskreten Finite-Elemente-Approximationen erster Ordnung entwickelt. Ein verallgemeinerter Ansatz drückt den Energiefehler durch Dualnormen eines oder mehrerer Residuen aus. Hinzu kommen berechenbare Zusatzterme, wie Oszillationen der gegebenen Daten, mit expliziten Konstanten. Für die Abschätzung der Dualnormen der Resi

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4

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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5

Ainsworth, Mark. "A posteriori error estimation in the finite element method." Thesis, Durham University, 1989. http://etheses.dur.ac.uk/6326/.

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The work broadly consists of two parts. In the first part we construct a framework for analyzing and developing a posteriori error estimators for use in the finite element solution of elliptic partial differential equations which have smooth solutions. The analysis makes use of complementary variational principles and the superconvergence phenomenon associated with the finite element method. The second part generalizes these results to the important case when the solution of the boundary value problem contains singularities. It is shown how the classical techniques may be easily modified to pe

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6

Köhler, Karoline Sophie. "On efficient a posteriori error analysis for variational inequalities." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17635.

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Effiziente und zuverlässige a posteriori Fehlerabschätzungen sind eine Hauptzutat für die effiziente numerische Berechnung von Lösungen zu Variationsungleichungen durch die Finite-Elemente-Methode. Die vorliegende Arbeit untersucht zuverlässige und effiziente Fehlerabschätzungen für beliebige Finite-Elemente-Methoden und drei Variationsungleichungen, nämlich dem Hindernisproblem, dem Signorini Problem und dem Bingham Problem in zwei Raumdimensionen. Die Fehlerabschätzungen hängen vom zum Problem gehörenden Lagrange Multiplikator ab, der eine Verbindung zwischen der Variationsungleich

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7

Chow, Chak-On 1968. "On a posteriori finite element bound procedures for nonsymmetric Eigenvalue problems." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85266.

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8

Pled, Florent. "Vers une stratégie robuste et efficace pour le contrôle des calculs par éléments finis en ingénierie mécanique." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00776633.

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Ce travail de recherche vise à contribuer au développement de nouveaux outils d'estimation d'erreur globale et locale en ingénierie mécanique. Les estimateurs d'erreur globale étudiés reposent sur le concept d'erreur en relation de comportement à travers des techniques spécifiques de construction de champs admissibles, assurant l'aspect conservatif ou garanti de l'estimation. Une nouvelle méthode de construction de champs admissibles est mise en place et comparée à deux autres méthodes concurrentes, en matière de précision, coût de calcul et facilité d'implémentation dans les codes éléments fi

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9

Apel, Thomas, and Cornelia Pester. "Clément-type interpolation on spherical domains - interpolation error estimates and application to a posteriori error estimation." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601335.

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In this paper, a mixed boundary value problem for the Laplace-Beltrami operator is considered for spherical domains in $R^3$, i.e. for domains on the unit sphere. These domains are parametrized by spherical coordinates (\varphi, \theta), such that functions on the unit sphere are considered as functions in these coordinates. Careful investigation leads to the introduction of a proper finite element space corresponding to an isotropic triangulation of the underlying domain on the unit sphere. Error estimates are proven for a Clément-type interpolation operator, where appropriate, we

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10

Kunert, Gerd. "A posteriori error estimation for convection dominated problems on anisotropic meshes." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200255.

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A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that th

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11

Russant, Stuart. "A-posteriori error estimation using higher moments in computational fluid dynamics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/aposteriori-error-estimation-using-higher-moments-in-computational-fluid-dynamics(77bdb9c6-e99a-490d-9624-fdc61525d039).html.

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In industrial situations time is expensive and simulation accuracy is not always investigated because it requires grid refinement studies or other time consuming methods. With this in mind the goal of this research is to develop a method to assess the errors and uncertainties on computational fluid dynamics (CFD) simulations that can be adopted by industry to meet their requirements and time constraints. In a CFD calculation there are a number of sources of errors and uncertainties. An uncertainty is a potential deficiency that is due to a lack of knowledge of an activity of the modelling proc

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12

Giacomini, Matteo. "Quantitative a posteriori error estimators in Finite Element-based shape optimization." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX070/document.

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Les méthodes d’optimisation de forme basées sur le gradient reposent sur le calcul de la dérivée de forme. Dans beaucoup d’applications, la fonctionnelle coût dépend de la solution d’une EDP. Il s’en suit qu’elle ne peut être résolue exactement et que seule une approximation de celle-ci peut être calculée, par exemple par la méthode des éléments finis. Il en est de même pour la dérivée de forme. Ainsi, les méthodes de gradient en optimisation de forme - basées sur des approximations du gradient - ne garantissent pas a priori que la direction calculée à chaque itération soit effectivement une d

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13

Castellazzi, Giovanni <1975&gt. "Verification in computational structural mechanics: recovery-based a posteriori error estimation." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/441/1/Giovanni_Castellazzi.pdf.

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14

Castellazzi, Giovanni <1975&gt. "Verification in computational structural mechanics: recovery-based a posteriori error estimation." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/441/.

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15

Bacharach, Lucien. "Caractérisation des limites fondamentales de l'erreur quadratique moyenne pour l'estimation de signaux comportant des points de rupture." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS322/document.

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Cette thèse porte sur l'étude des performances d'estimateurs en traitement du signal, et s'attache en particulier à étudier les bornes inférieures de l'erreur quadratique moyenne (EQM) pour l'estimation de points de rupture, afin de caractériser le comportement d'estimateurs, tels que celui du maximum de vraisemblance (dans le contexte fréquentiste), mais surtout du maximum a posteriori ou de la moyenne conditionnelle (dans le contexte bayésien). La difficulté majeure provient du fait que, pour un signal échantillonné, les paramètres d'intérêt (à savoir les points de rupture) appartiennent à u

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16

Tempone, Olariaga Raul. "Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations." Doctoral thesis, KTH, Numerisk analys och datalogi, NADA, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3413.

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The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods. The first paper develops new expansions of the weakcomputational error for Ito stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a

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17

Wilkins, Catherine. "Adaptive finite element methods for the damped wave equation." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302398.

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18

Ohlberger, Mario. "A posteriori error estimates and adaptive methods for convection dominated transport processes." [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=961616245.

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19

Creusé, Emmanuel, Gerd Kunert, and Serge Nicaise. "A posteriori error estimation for the Stokes problem: Anisotropic and isotropic discretizations." Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200300057.

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The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail. Our analysis covers two- and three-dimensional domains, conforming and nonconforming discretizations as well as different elements. This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented. Lower and upper error bounds form

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20

Grepl, Martin A. (Martin Alexander) 1974. "Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32387.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.<br>Includes bibliographical references (p. 243-251).<br>Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a technique for the prediction of outputs of interest of parabolic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced-basis approximations - Galerkin projection onto a space WN spanned by s

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21

Mavriplis, Cathy. "Nonconforming discretizations and a posteriori error estimators for adaptive spectral element techniques." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14526.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1989.<br>Includes bibliographical references (leaves 151-157).<br>by Catherine Andria Mavriplis.<br>Ph.D.

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22

Simões, Eduardo Tenório. "Linear and nonlinear hirarchical plate models and a posteriori kinematical error estimator." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/3/3144/tde-26072016-151855/.

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This study explores the use of hierarchical models to represent three-dimensional solids in a computationally inexpensive way. First, it is investigated the choice of the finite element spaces and how it affects the convergence in relation to the thickness parameter. It was studied three different models. It was shown that the best lowest order suitable combination of spaces grows in all fields as the model order is enriched. After, it is presented a theory to evaluate the error in the discretization and the kinematical hypothesis. It is shown that the implemented error in discretization techn

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23

Kunert, Gerd. "A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes." Doctoral thesis, [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10324701.

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24

Ren, Chengfang. "Caractérisation des performances minimales d'estimation pour des modèles d'observations non-standards." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112167/document.

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Dans le contexte de l'estimation paramétrique, les performances d'un estimateur peuvent être caractérisées, entre autre, par son erreur quadratique moyenne (EQM) et sa résolution limite. La première quantifie la précision des valeurs estimées et la seconde définit la capacité de l'estimateur à séparer plusieurs paramètres. Cette thèse s'intéresse d'abord à la prédiction de l'EQM "optimale" à l'aide des bornes inférieures pour des problèmes d'estimation simultanée de paramètres aléatoires et non-aléatoires (estimation hybride), puis à l'extension des bornes de Cramér-Rao pour des modèles d'obse

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25

Ludwig, Marcus John. "Finite element error estimation and adaptivity for problems of elasticity." Thesis, Brunel University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246151.

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26

Zhu, Liang. "Robust a posteriori error estimation for discontinuous Galerkin methods for convection diffusion problems." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/23337.

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The present thesis is concerned with the development and practical implementation of robust a-posteriori error estimators for discontinuous Galerkin (DG) methods for convection-diffusion problems. It is well-known that solutions to convection-diffusion problems may have boundary and internal layers of small width where their gradients change rapidly. A powerful approach to numerically resolve these layers is based on using hp-adaptive finite element methods, which control and minimize the discretization errors by locally adapting the mesh sizes (h-refinement) and the approximation orders (p-r

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27

Bridgeman, Leila. "Stability and a posteriori error analysis of discontinious Galerkin methods for linearized elasticity." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=95054.

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We consider discontinuous Galerkin finite element methods for the discretization of linearized elasticity problems in two space dimensions. Inf-sup stability results on the continuous and discrete level are provided. Furthermore, we derive lower and upper a posteriori error bounds that are robust with respect to nearly incompressible materials, and can easily be implemented within an automatic mesh refinement procedure. The theoretical results are illustrated with a series of numerical experiments.<br>Nous considérons les méthodes de Galerkin pour la discrétisation des relations déformations-d

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28

Andrews, J. G. "An a posteriori error indicator and its application to adaptive methods in CFD." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319051.

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29

Effland, Alexander [Verfasser]. "Discrete Riemannian Calculus and A Posteriori Error Control on Shape Spaces / Alexander Effland." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1150777796/34.

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30

Yu, Peng. "Isogeometric analysis with local adaptivity based on a posteriori error estimation for elastodynamics." Thesis, Cardiff University, 2019. http://orca.cf.ac.uk/119867/.

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IsoGeometric Analysis (IGA) was invented to integrate the Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) into a unified process. According to the recent research, IGA performs a super convergence in case of vibration, and especially, it perfectly addresses the Gibbs phenomenon (fluctuation) occurring in discrete spectra when using standard Finite Element Method (FEM). However, due to the tensor-product structure of Non-Uniform Rational B-Splines (NURBS), it fails to achieve the local refinement, which restricts its application to engineering fields performing local characteri

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31

Lins, Rafael Marques. "A posteriori error estimations for the generalized finite element method and modified versions." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-03092015-083839/.

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This thesis investigates two a posteriori error estimators, based on gradient recovery, aiming to fill the gap of the error estimations for the Generalized FEM (GFEM) and, mainly, its modified versions called Corrected XFEM (C-XFEM) and Stable GFEM (SGFEM). In order to reach this purpose, firstly, brief reviews regarding the GFEM and its modified versions are presented, where the main advantages attributed to each numerical method are highlighted. Then, some important concepts related to the error study are presented. Furthermore, some contributions involving a posteriori error estimations for

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32

Buß, Hinderk M. "A posteriori error estimators based on duality techniques from the calculus of variations." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10790752.

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33

ElSheikh, Ahmed H. Chidiac S. E. Smith Spencer B. "Multiscale a posteriori error estimation and mesh adaptivity for reliable finite element analysis." *McMaster only, 2007.

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34

Houston, Paul D. "Lagrange-Galerkin methods for unsteady convection-diffusion problems : a posteriori error analysis and adaptivity." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337607.

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35

Kunert, Gerd [Verfasser]. "A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes / Gerd Kunert." Chemnitz : Universitätsbibliothek Chemnitz, 1999. http://d-nb.info/1210931834/34.

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36

Moldenhauer, Marcel [Verfasser], and Gerhard [Akademischer Betreuer] Starke. "Stress reconstruction and a-posteriori error estimation for elasticity / Marcel Moldenhauer ; Betreuer: Gerhard Starke." Duisburg, 2020. http://d-nb.info/1221061712/34.

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37

Lin, Shan. "Analysing Generalisation Error Bounds For Convolutional Neural Networks." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/20315.

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Analysing Generalisation Error Bounds for Convolutional Neural Networks Abstract: Convolutional neural networks (CNNs) have achieved breakthrough performance in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterising the generalisability of neural networks has mostly focused on fully connected neural networks (FNNs), with CNNs regarded as a special case of FNNs without taking into account the special structure of convolutional layers; therefore, the CNN bounds may not be as tight as in FNNs. Here we propose a

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38

Kieweg, Michael. "An a posteriori error analysis for distributed elliptic optimal control problems with pointwise state constraints." kostenfrei kostenfrei, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:384-opus-7184.

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Pester, Cornelia. "A residual a posteriori error estimator for the eigenvalue problem for the Laplace-Beltrami operator." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601556.

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The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in $\R^3$. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the spherical domains and a carefully chosen finite element discretization allows us to use an approach similar to the one for the two-dimensional case. In order to assure results in the quality of those for plane domains, weighted norms

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Wu, Heng. "An a-posteriori finite element error estimator for adaptive grid computation of viscous incompressible flows." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape2/PQDD_0021/NQ53797.pdf.

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Trenz, Stefan [Verfasser]. "POD-Based A-posteriori Error Estimation for Control Problems Governed by Nonlinear PDEs / Stefan Trenz." Konstanz : Bibliothek der Universität Konstanz, 2017. http://d-nb.info/1142113868/34.

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Brenner, Andreas [Verfasser], Eberhard [Gutachter] Bänsch, and Charalambos [Gutachter] Makridakis. "A-posteriori error estimates for pressure-correction schemes / Andreas Brenner ; Gutachter: Eberhard Bänsch, Charalambos Makridakis." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2016. http://d-nb.info/1114499692/34.

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43

Kirby, Robert Charles. "Local time stepping and a posteriori error estimates for flow and transport in porous media /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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44

Kunert, Gerd. "Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes." Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000867.

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We consider a singularly perturbed reaction-diffusion problem and derive and rigorously analyse an a posteriori residual error estimator that can be applied to anisotropic finite element meshes. The quotient of the upper and lower error bounds is the so-called matching function which depends on the anisotropy (of the mesh and the solution) but not on the small perturbation parameter. This matching function measures how well the anisotropic finite element mesh corresponds to the anisotropic problem. Provided this correspondence is sufficiently good, the matching function is O(1). Hence one obt

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Grosman, Serguei. "The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601418.

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. The simplest local error estimator from the implementation point of view is the so-called hierarchical error estimator. The reliability proof is usual

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Kunert, Gerd. "A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100730.

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The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three modifications of these estimators are introduced and discussed. Numerical experiments for all estimators complement and confirm the theoretical results.

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Grosz, Lutz [Verfasser]. "A-posteriori error estimates for the finite element solution on non-linear variational problems / Lutz Grosz." Karlsruhe : KIT-Bibliothek, 1997. http://d-nb.info/1013872436/34.

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48

Lu, James 1977. "An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34134.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.<br>Includes bibliographical references (leaves 169-178).<br>Introduction: Aerodynamic design optimization has seen significant development over the past decade. Adjoint-based shape design for elliptic systems was first proposed by Pironneau and applied to transonic flow by Jameson . A review of the aerodynamic shape optimization literature and a large list of references is given in. Over the years much technology has been developed, allowing engineers to contemplate applying optimization method

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Sen, Sugata 1977. "Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/39355.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2007.<br>Includes bibliographical references (p. 251-261).<br>Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a general methodology for the predicition of outputs of interest of non-coercive elliptic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced basis approximations - Galerkin pro

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Frankenbach, Matthias [Verfasser]. "An Adjoint Based A Posteriori Error Estimator for Moving Meshes in Large Eddy Simulations / Matthias Frankenbach." München : Verlag Dr. Hut, 2014. http://d-nb.info/1055863877/34.

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