𝐻¹-Superconvergence of a difference finite element method based on the 𝑃₁-𝑃₁-conforming element on non-uniform meshes for the 3D Poisson equation

DOI10.1090/mcom/3266zbMath1471.65171OpenAlexW2741560340MaRDI QIDQ4637574

Xinlong Feng, Ruijian He, Zhang-Xin Chen

Publication date: 24 April 2018

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

Full work available at URL: https://doi.org/10.1090/mcom/3266

zbMATH Keywords

non-uniform mesh3D Poisson equationdifference finite element method\(H^1\)-superconvergence\(P_1\)-conforming element

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items

Difference Finite Element Method for the 3D Steady Navier–Stokes Equations, A stabilized difference finite element method for the 3D steady Stokes equations, A second-order maximum bound principle preserving operator splitting method for the Allen-Cahn equation with applications in multi-phase systems, A stabilized difference finite element method for the 3D steady incompressible Navier-Stokes equations, Superconvergence of numerical gradient for weak Galerkin finite element methods on nonuniform Cartesian partitions in three dimensions, Superconvergence in \(H^1\)-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh, Difference finite element method for the 3D steady Stokes equations

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