LOCATING NATURAL SUPERCONVERGENT POINTS OF FINITE ELEMENT METHODS IN 3D

Keywords

Superconvergence, Finite element method, Polynomial, Mathematics, Natural (archaeology)

References

• SUPERCONVERGENCE OF TETRAHEDRAL QUADRATIC FINITE ELEMENTSJanBrandts, MichalKǐízek — 2005
• Finite element methods: superconvergence, post-processing, and a posteriori estimatesM. Křížek, P. Neittaanmäki, R. Stenberg — 1998
• Harmonic Function TheorySheldon Axler, Paul Bourdon, Wade Ramey — 1992
• Derivative superconvergent points in finite element solutions of Poisson's equation for the serendipity and intermediate families - a theoretical justificationZhimin Zhang — 1998
• Superconvergence for galerkin methods for the two point boundary problem via local projectionsJim Douglas, Todd Dupont — 1973
• Superconvergence in finite element methods and meshes that are locally symmetric with respect to a pointA. H. Schatz, Ian H. Sloan, Lars B. Wahlbin — 1996
• Derivative superconvergent points in finite element solutions of harmonic functions- A theoretical justificationZhimin Zhang — 2002
• Natural superconvergent points of triangular finite elementsRunchang Lin, Zhimin Zhang — 2004
• On superconvergence techniquesMichal Křı́žek, Pekka Neittaanmäki — 1987
• Pointwise superconvergence of the gradient for the linear tetrahedral elementG. Goodsell — 1994
• Computer‐based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equationsIvo Babuška, T. Strouboulis, C.S. Upadhyay — 1996
• A Posteriori Error Estimation in Finite Element AnalysisMark Ainsworth, J. Tinsley Oden — 2000
• Finite Element AnalysisD. Monthei — 1999

Cited by

• The Cell Method: quadratic interpolation with tetrahedra for 3D scalar fieldsMartino Pani, Fulvia Taddei — 2013
• High accuracy analysis of tensor-product linear pentahedral finite elements for variable coefficient elliptic equationsJinghong Liu, Yijun Deng, Qiding Zhu — 2012
• Pointwise supercloseness of the displacement for tensor-product quadratic pentahedral finite elementsJinghong Liu — 2012
• Natural Superconvergence Points in Three-Dimensional Finite ElementsRunchang Lin, Zhimin Zhang — 2008
• Convergence Analysis for Cubic Serendipity Finite Elements with Thirty-Two Degrees of FreedomJing Hong Liu, Xiao Cheng Huo — 2011
• Superconvergence of tetrahedral quadratic finite elements for a variable coefficient elliptic equationJinghong Liu, Gui Wu Hu, Qiding Zhu — 2013
• Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph TypeQiumei Huang, Hehu Xie, Hermann Brunner — 2011
• An estimate for the three-dimensional discrete Green's function and applicationsJinghong Liu, Bo Jia, Qiding Zhu — 2010
• Superconvergence of tricubic block finite elementsJinghong Liu, Haina Sun, QiDing Zhu — 2009
• Maximum Norm Error Estimates for Quadratic Block Finite Elements with Twenty-Six Degrees of FreedomJing Hong Liu, Gui Wu Hu — 2011
• Pointwise supercloseness of quadratic serendipity block finite elements for a variable coefficient elliptic equationJinghong Liu, Xiaocheng Huo, Qiding Zhu — 2011
• Pointwise supercloseness of pentahedral finite elementsJinghong Liu, Qiding Zhu — 2010
• Pointwise supercloseness of tensor‐product block finite elementsJinghong Liu, Qiding Zhu — 2009
• Superconvergence Recovery for the Gradient of the Trilinear Finite ElementJing Hong Liu, De Cheng Yin — 2011
• Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph TypeXiuxiu Xu, Qiumei Huang, Hongtao Chen — 2016
• NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR, BILINEAR, AND TRILINEAR FE APPROXIMATIONSAntti Hannukainen, Sergey Korotov null, Michal Křížek — 2009
• H1-Superconvergence of a difference finite element method based on the P1-P1-conforming element on non-uniform meshes for the 3D Poisson equationRuijian He, Xinlong Feng, Zhangxin Chen — 2018
• Higher-order approximations in the finite element methodsK. Kolman — 2010
• H1‐superconvergence of finite difference method based on Q1‐element on quasi‐uniform mesh for the 3D Poisson equationXinlong Feng, Ruijian He, Zhangxin Chen — 2019
• Locally pointwise superconvergence of the tensor-product finite element in three dimensionsJinghong Liu, Wen Liu, Qiding Zhu — 2019

Related papers

• Superconvergence in finite element methods and meshes that are locally symmetric with respect to a pointA. H. Schatz, Ian H. Sloan, Lars B. Wahlbin — 1996
• Gradient superconvergence on uniform simplicial partitions of polytopesJ.H. Brandts — 2003
• Pointwise superconvergence of the gradient for the linear tetrahedral elementG. Goodsell — 1994
• Natural Superconvergence Points in Three-Dimensional Finite ElementsRunchang Lin, Zhimin Zhang — 2008
• History and future of superconvergence in three-dimensional finite element methodsJan Brandts — 2001
• Superconvergence for tetrahedral quadratic finite element methods for elliptic equationsJan Brandts, Michal Křı́žek — 2005
• SUPERCONVERGENCE OF TETRAHEDRAL QUADRATIC FINITE ELEMENTSJanBrandts, MichalKǐízek — 2005
• Maximum‐norm superapproximation of the gradient for the trilinear block finite elementJinghong Liu, Qiding Zhu — 2007
• Pointwise supercloseness of tensor‐product block finite elementsJinghong Liu, Qiding Zhu — 2009
• Superconvergence of tetrahedral linear finite elementsL Chen — 2006