Natural superconvergent points of triangular finite elements

DOI10.1002/num.20013zbMath1068.65123OpenAlexW2045633883MaRDI QIDQ4651868

Runchang Lin, Zhimin Zhang

Publication date: 23 February 2005

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1011&context=math_reports

zbMATH Keywords

finite element methodnumerical examplesGram-Schmidt orthogonalizationLaplace equationPoisson equationtriangular elementsnatural superconvergence

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Global \(L^2\) superconvergence of the tetrahedral quadratic finite element, Ultraconvergence of Finite Element Method by Richardson Extrapolation for Elliptic Problems with Constant Coefficients, Centroidal Voronoi tessellation-based finite element superconvergence, Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems, Unnamed Item, The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain, The highest order superconvergence for bi-$k$ degree rectangular elements at nodes: A proof of $2k$-conjecture, Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations

Cites Work

• Superconvergence in Galerkin finite element methods
• Superconvergence of the gradient for quadratic triangular finite elements
• 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 equations