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Relevant bibliographies by topics / Least-Squares Finite Element Method

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Academic literature on the topic 'Least-Squares Finite Element Method'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Least-Squares Finite Element Method"

1

Musivand-Arzanfudi, M., and H. Hosseini-Toudeshky. "Moving least-squares finite element method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 9 (2007): 1019–36. http://dx.doi.org/10.1243/09544062jmes463.

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A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for

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Keith, Brendan, Socratis Petrides, Federico Fuentes, and Leszek Demkowicz. "Discrete least-squares finite element methods." Computer Methods in Applied Mechanics and Engineering 327 (December 2017): 226–55. http://dx.doi.org/10.1016/j.cma.2017.08.043.

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Chen, Fuchen, Eric Chung, and Lijian Jiang. "Least-squares mixed generalized multiscale finite element method." Computer Methods in Applied Mechanics and Engineering 311 (November 2016): 764–87. http://dx.doi.org/10.1016/j.cma.2016.09.010.

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Jiang, Bo-Nan, and Louis A. Povinelli. "Least-squares finite element method for fluid dynamics." Computer Methods in Applied Mechanics and Engineering 81, no. 1 (1990): 13–37. http://dx.doi.org/10.1016/0045-7825(90)90139-d.

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Chaudhry, Jehanzeb H., Luke N. Olson, and Peter Sentz. "A Least-Squares Finite Element Reduced Basis Method." SIAM Journal on Scientific Computing 43, no. 2 (2021): A1081—A1107. http://dx.doi.org/10.1137/20m1323552.

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Duan, Huo-Yuan, and Guo-Ping Liang. "Nonconforming elements in least-squares mixed finite element methods." Mathematics of Computation 73, no. 245 (2003): 1–18. http://dx.doi.org/10.1090/s0025-5718-03-01520-5.

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Westphal, Chad. "A least-squares finite-element method for viscoelastic fluids." PAMM 7, no. 1 (2007): 1025101–2. http://dx.doi.org/10.1002/pamm.200700141.

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Jiang, Bo-Nan, and Louis A. Povinelli. "Optimal least-squares finite element method for elliptic problems." Computer Methods in Applied Mechanics and Engineering 102, no. 2 (1993): 199–212. http://dx.doi.org/10.1016/0045-7825(93)90108-a.

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Bochev, Pavel B., and Max D. Gunzburger. "Finite Element Methods of Least-Squares Type." SIAM Review 40, no. 4 (1998): 789–837. http://dx.doi.org/10.1137/s0036144597321156.

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Kumar, Rajeev, and Brian H. Dennis. "Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport." Differential Equations and Nonlinear Mechanics 2008 (2008): 1–21. http://dx.doi.org/10.1155/2008/267454.

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The least-squares finite element method (LSFEM) has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM). The method leads to a minimization problem in theL2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilizati

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Dissertations / Theses on the topic "Least-Squares Finite Element Method"

1

Bringmann, Philipp. "Adaptive least-squares finite element method with optimal convergence rates." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22350.

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Die Least-Squares Finite-Elemente-Methoden (LSFEMn) basieren auf der Minimierung des Least-Squares-Funktionals, das aus quadrierten Normen der Residuen eines Systems von partiellen Differentialgleichungen erster Ordnung besteht. Dieses Funktional liefert einen a posteriori Fehlerschätzer und ermöglicht die adaptive Verfeinerung des zugrundeliegenden Netzes. Aus zwei Gründen versagen die gängigen Methoden zum Beweis optimaler Konvergenzraten, wie sie in Carstensen, Feischl, Page und Praetorius (Comp. Math. Appl., 67(6), 2014) zusammengefasst werden. Erstens scheinen fehlende Vorfaktoren proport

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2

Johnsen, Eivind. "Application method of the least squares finite element method to fracture mechanics." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/16435.

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Goktolga, Mustafa Ugur. "Simulation Of Conjugate Heat Transfer Problems Using Least Squares Finite Element Method." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614787/index.pdf.

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In this thesis study, a least-squares finite element method (LSFEM) based conjugate heat transfer solver was developed. In the mentioned solver, fluid flow and heat transfer computations were performed separately. This means that the calculated velocity values in the flow calculation part were exported to the heat transfer part to be used in the convective part of the energy equation. Incompressible Navier-Stokes equations were used in the flow simulations. In conjugate heat transfer computations, it is required to calculate the heat transfer in both flow field and solid region. In this study,

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Bringmann, Philipp [Verfasser]. "Adaptive least-squares finite element method with optimal convergence rates / Philipp Bringmann." Berlin : Humboldt-Universität zu Berlin, 2021. http://d-nb.info/1226153186/34.

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Storn, Johannes. "Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20141.

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Aufgrund der fundamentalen Bedeutung partieller Differentialgleichungen zur Beschreibung von Phänomenen in angewandten Wissenschaften ist deren Analyse ein Kerngebiet der Mathematik. Durch Computer lassen sich die Lösungen für eine Vielzahl dieser Gleichungen näherungsweise bestimmen. Die dabei verwendeten numerischen Verfahren sollen auf möglichst exakte Approximationen führen und deren Genauigkeit verifizieren. Die Least-Squares Finite-Elemente-Methode (LSFEM) und die unstetige Petrov-Galerkin (DPG) Methode sind solche Verfahren. Sie werden in dieser Dissertation untersucht. Der erste Tei

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Prabhakar, Vivek. "Least squares based finite element formulations and their applications in fluid mechanics." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1152.

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Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.

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Wei, Fei. "Weighted least-squares finite element methods for PIV data assimilation." Thesis, Montana State University, 2011. http://etd.lib.montana.edu/etd/2011/wei/WeiF0811.pdf.

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The ability to diagnose irregular flow patterns clinically in the left ventricle (LV) is currently very challenging. One potential approach for non-invasively measuring blood flow dynamics in the LV is particle image velocimetry (PIV) using microbubbles. To obtain local flow velocity vectors and velocity maps, PIV software calculates displacements of microbubbles over a given time interval, which is typically determined by the actual frame rate. In addition to the PIV, ultrasound images of the left ventricle can be used to determine the wall position as a function of time, and the inflow and o

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Akargun, Yigit Hayri. "Least-squares Finite Element Solution Of Euler Equations With Adaptive Mesh Refinement." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614138/index.pdf.

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Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also ap

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Danisch, Garvin. "Gemischte Finite-element-least-squares-Methoden für die Flachwassergleichungen mit kleiner Viskosität." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983833052.

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Books on the topic "Least-Squares Finite Element Method"

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D, Gunzburger Max, ed. Least-squares finite element methods. Springer, 2009.

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Bochev, Pavel B. Least-squares finite element methods. Springer, 2009.

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Bochev, Pavel B. Least-squares finite element methods. Springer, 2009.

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Jiang, Bo-nan. The Least-Squares Finite Element Method. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03740-9.

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Gunzburger, Max D., and Pavel B. Bochev. Least-Squares Finite Element Methods. Springer New York, 2009. http://dx.doi.org/10.1007/b13382.

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6

Jiang, Bo-Nan. Least-squares finite elements for Stokes problem. ICOMP, 1988.

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Jiang, Bo-nan. Least-squares finite element method for fluid dynamics. Institute for Computational Mechanics in Propulsion, 1989.

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8

Bochev, Pavel B. Accuracy of least-squares method for the Navier-Stokes equations. National Aeronautics and Space Administration, 1993.

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Bochev, Pavel B. Accuracy of least-squares method for the Navier-Stokes equations. National Aeronautics and Space Administration, 1993.

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Bochev, Pavel B. Accuracy of least-squares method for the Navier-Stokes equations. National Aeronautics and Space Administration, 1993.

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Book chapters on the topic "Least-Squares Finite Element Method"

1

Bochev, Pavel, and Max Gunzburger. "Least Squares Finite Element Methods." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_330.

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Jiang, Bonan, and Guojun Liao. "The Least-Squares Meshfree Finite Element Method." In Computational Mechanics. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75999-7_141.

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Bochev, Pavel B., and Max D. Gunzburger. "Variations on Least-Squares Finite Element Methods." In Applied Mathematical Sciences. Springer New York, 2009. http://dx.doi.org/10.1007/b13382_12.

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Bochev, Pavel B., and Max D. Gunzburger. "Mathematical Foundations of Least-Squares Finite Element Methods." In Applied Mathematical Sciences. Springer New York, 2009. http://dx.doi.org/10.1007/b13382_3.

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Starke, Gerhard. "Adaptive Least Squares Finite Element Methods in Elasto-Plasticity." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12535-5_80.

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Kot, John. "An Investigation of the Least-Squares Finite Element Method in Electromagnetism." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM). Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-44873-0_19.

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Palha, Artur, and Marc Gerritsma. "Mimetic Least-Squares Spectral/hp Finite Element Method for the Poisson Equation." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12535-5_79.

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Mallet, M. "Contribution to Problem III using a Galerkin Least Squares Finite Element Method." In Hypersonic Flows for Reentry Problems. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77922-0_29.

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Bochev, Pavel B., and Max D. Gunzburger. "The Agmon–Douglis–Nirenberg Setting for Least-Squares Finite Element Methods." In Applied Mathematical Sciences. Springer New York, 2009. http://dx.doi.org/10.1007/b13382_4.

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Adler, J. H., and P. S. Vassilevski. "Improving Conservation for First-Order System Least-Squares Finite-Element Methods." In Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7172-1_1.

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Conference papers on the topic "Least-Squares Finite Element Method"

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Liang, Shin-Jye. "A Least-Squares Finite-Element Method for Shallow-Water Equations." In OCEANS 2008 - MTS/IEEE Kobe Techno-Ocean. IEEE, 2008. http://dx.doi.org/10.1109/oceanskobe.2008.4531097.

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Hou, Lin-Jun. "A time-accurate least-squares finite element method for incompressible flow." In 33rd Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-81.

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3

Kumar, Rajeev, and Brian H. Dennis. "The Least-Squares Galerkin Split Finite Element Method for Buoyancy-Driven Flow." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29157.

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The least-squares finite element method (LSFEM), based on minimizing the l2-norm of the residual is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike Galerkin finite element method (GFEM). However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of

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4

Rasmussen, Cody, Robert Canfield, and J. Reddy. "The Least-Squares Finite Element Method Applied to Fluid-Structure Interation Problems." In 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-2407.

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French, Donald A., Christopher R. Schrock, and John A. Benek. "Least squares overset finite element method for scalar hyperbolic problems in 2D." In 23rd AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-4277.

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JIANG, BO-NAN, T. LIN, LIN-JUN HOU, and LOUIS POVINELLI. "A least-squares finite element method for 3D incompressible Navier-Stokes equations." In 31st Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-338.

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7

Kumar, Rajeev, and Brian H. Dennis. "A Least-Squares/Galerkin Finite Element Method for Incompressible Navier-Stokes Equations." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49654.

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The least-squares finite element method (LSFEM), which is based on minimizing the l2-norm of the residual, has many attractive advantages over Galerkin finite element method (GFEM). It is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike GFEM. However, the higher continuity requirements for second-order terms in the governing equations force the

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Thompson, Lonny L., and Prapot Kunthong. "A Residual Based Variational Method for Reducing Dispersion Error in Finite Element Methods." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80551.

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A difficulty of the standard Galerkin finite element method has been the ability to accurately resolve oscillating wave solutions at higher frequencies. Many alternative methods have been developed including high-order methods, stabilized Galerkin methods, multi-scale variational methods, and other wave-based discretization methods. In this work, consistent residuals, both in the form of least-squares and gradient least-squares are linearly combined and added to the Galerkin variational Helmholtz equation to form a new generalized Galerkin least-squares method (GGLS). By allowing the stabiliza

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Kumar, Rajeev, and Brian H. Dennis. "A Least-Squares Galerkin Split Finite Element Method for Compressible Navier-Stokes Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87569.

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A novel finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by a pure LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the least-squares method. Resulting system matrix is always symmetric and positive definite and can be solved by iterative solvers like pre-conditioned conjugate gradient method. The method is stable for convection-dominated flows and allows f

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Yu, Sheng-Tao, Bo-Nan Jiang, Nan-Suey Liu, and Jie Wu. "Simulation of an H2/O2 flame by the least-squares finite element method." In 30th Joint Propulsion Conference and Exhibit. American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/6.1994-3046.

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Reports on the topic "Least-Squares Finite Element Method"

1

CAPACITY EVALUATION OF EIGHT BOLT EXTENDED ENDPLATE MOMENT CONNECTIONS SUBJECTED TO COLUMN REMOVAL SCENARIO. The Hong Kong Institute of Steel Construction, 2021. http://dx.doi.org/10.18057/ijasc.2021.17.3.6.

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The extended stiffened endplate (8ES) connection is broadly used in the seismic load-resisting parts of steel structures. This connection is prequalified based on the AISC 358 standard, especially for seismic regions. To study this connection’s behaviors, in the event of accidental loss of a column, the finite element model results were verified against the available experimental data. A parametric study using the finite element method was then carried out to investigate these numerical models’ maximum capacity and effective parameters' effect on their maximum capacity in a column loss scenari

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