Remarks on a posteriori error estimation for finite element solutions

DOI10.1016/j.cam.2005.07.031zbMath1109.65094OpenAlexW2042673351MaRDI QIDQ861895

Fumio Kikuchi, Hironobu Saito

Publication date: 2 February 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.07.031

zbMATH Keywords

numerical examplesfinite elementerror boundPoisson equationhypercircle method\(P_{1}\) triangular elementRaviart-Thomas triangular element

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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 (6)

Computational Lower Bounds of the Maxwell Eigenvalues ⋮ Guaranteed local error estimation for finite element solutions of boundary value problems ⋮ A novel lattice Boltzmann model for the Poisson equation ⋮ Computable interpolation error constants for the geometric simplex finite elements ⋮ Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations ⋮ Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains

Cites Work

• A simple error estimator and adaptive procedure for practical engineerng analysis
• Mixed and Hybrid Finite Element Methods
• Explicit error bounds in a conforming finite element method
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