Superconvergence of high order finite difference schemes based on variational formulation for elliptic equations

DOI10.1007/s10915-020-01144-wzbMath1434.65268arXiv1904.01179OpenAlexW3003548368MaRDI QIDQ2302381

Xiangxiong Zhang, Hao Li

Publication date: 26 February 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01179

zbMATH Keywords

superconvergenceelliptic equationsGauss-Lobatto quadraturefinite difference scheme based on variational formulationhigh order accurate discrete Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) 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) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations ⋮ Positivity preserving temporal second-order spatial fourth-order conservative characteristic methods for convection dominated diffusion equations ⋮ Accuracy of Spectral Element Method for Wave, Parabolic, and Schrödinger Equations ⋮ On the monotonicity and discrete maximum principle of the finite difference implementation of \(C^0\)-\(Q^2\) finite element method

Cites Work

• A note on \(C^ 0\) Galerkin methods for two-point boundary problems
• Regularity results for elliptic equations in Lipschitz domains
• Superconvergence of quadratic finite elements on mildly structured grids
• Superconvergence of the gradient of finite element solutions
• Algebraic multigrid methods
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