\(H^1\)-super-convergence of center finite difference method based on \(P_1\)-element for the elliptic equation

DOI10.1016/J.APM.2014.04.033zbMath1429.65268OpenAlexW1973538424MaRDI QIDQ1634142

Xinlong Feng, Yin-Nian He

Publication date: 17 December 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2014.04.033

zbMATH Keywords

stabilityelliptic equationnon-uniform meshsuper-convergencecenter finite difference method

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)

Related Items (5)

A stabilized difference finite element method for the 3D steady Stokes equations ⋮ A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos ⋮ A theoretical analysis of a new second order finite volume approximation based on a low-order scheme using general admissible spatial meshes for the one dimensional wave equation ⋮ Superconvergence in \(H^1\)-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh ⋮ 𝐻¹-Superconvergence of a difference finite element method based on the 𝑃₁-𝑃₁-conforming element on non-uniform meshes for the 3D Poisson equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A generalization of the vertex-centered finite volume scheme to arbitrary high order
• On the finite volume element method
• Supraconvergent cell-centered scheme for two dimensional elliptic problems
• Analysis of linear and quadratic simplicial finite volume methods for elliptic equations
• On first and second order box schemes
• Quadratic convergence for cell-centered grids
• On the supraconvergence of elliptic finite difference schemes
• Development and analysis of higher order finite volume methods over rectangles for elliptic equations
• \(P _{1}\)-nonconforming quadrilateral finite volume methods for the semilinear elliptic equations
• A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
• The Finite Volume Element Method for Diffusion Equations on General Triangulations
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degreepon Unstructured Grids
• Some Error Estimates for the Box Method
• The Numerical Solution of Second-Order Boundary Value Problems on Nonuniform Meshes
• On Convergence of Block-Centered Finite Differences for Elliptic Problems
• Convergence of Finite Volume Schemes for Poisson’s Equation on Nonuniform Meshes
• Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences
• Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
• Connection between finite volume and mixed finite element methods
• H¹-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation
• Convergence of a Compact Scheme for the Pure Streamfunction Formulation of the Unsteady Navier–Stokes System
• Supraconvergence and Supercloseness of a Scheme for Elliptic Equations on Nonuniform Grids
• Supraconvergence of a finite difference scheme for solutions in Hs(0, L)

This page was built for publication: \(H^1\)-super-convergence of center finite difference method based on \(P_1\)-element for the elliptic equation