A review of some a posteriori error estimates for adaptive finite element methods

DOI10.1016/j.matcom.2008.12.019zbMath1196.65173OpenAlexW2030230799MaRDI QIDQ991482

Karel Segeth

Publication date: 7 September 2010

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2008.12.019

zbMATH Keywords

nonlinear parabolic equationbiharmonic equationPoisson equationa posteriori error estimatorssecond order elliptic equation\(hp\)-adaptive finite element methodstationary Navier-Stokes equationcomputational error estimatesquasilinear second order equationsstationary convection-diffusion-reaction equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40) Error bounds for boundary value problems involving PDEs (65N15) Navier-Stokes equations (35Q30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Quasilinear elliptic equations (35J62)

Related Items (10)

On a posteriori error estimation using distances between numerical solutions and angles between truncation errors ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation ⋮ A hierarchically enhanced recovery-based error estimator for bidimensional elastoplastic modelling by generalized finite element approach ⋮ A posteriori error estimates and an adaptive finite element solution for the system of unsteady convection-diffusion-reaction equations in fluidized beds ⋮ An adaptive mesh refinement strategy for finite element solution of the elliptic problem ⋮ A modified bubble placement method and its application in solving elliptic problem with discontinuous coefficients adaptively ⋮ On the Advantages and Drawbacks of A Posteriori Error Estimation for Fourth-Order Elliptic Problems ⋮ Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities ⋮ Interplay between discretization and algebraic computation in adaptive numerical solutionof elliptic PDE problems

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