Derivative superconvergent points in finite element solutions of harmonic functions--- A theoretical justification

DOI10.1090/S0025-5718-01-01398-9zbMath1007.65081OpenAlexW2026118076MaRDI QIDQ3147168

Zhimin Zhang

Publication date: 18 September 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01398-9

zbMATH Keywords

finite elementPoisson's equationharmonic functionsuperconvergenceLaplace equation

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 (7)

Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods ⋮ Superconvergence in \(H^1\)-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh ⋮ Superconvergence in the generalized finite element method ⋮ 𝐻¹-Superconvergence of a difference finite element method based on the 𝑃₁-𝑃₁-conforming element on non-uniform meshes for the 3D Poisson equation ⋮ Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis ⋮ 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

Cites Work

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• Superconvergence in Galerkin finite element methods
• Derivative superconvergent points in finite element solutions of Poisson’s equation for the serendipity and intermediate families - a theoretical justification
• Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
• 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

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