A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods

Authors:
Emmanuel Creusé;Serge Nicaise
Affiliations:
Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé UMR 8524, EPI SIMPAF - INRIA Lille Nord Europe, UFR de Mathématiques Pures et Appliquées, Cité ...;Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques de Valenciennes, F-59313 - Valenciennes Cedex 9, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 11
Cited 0

A posteriori error indicators for Maxwell's equations

Journal of Computational and Applied Mathematics
Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: a smooth problem and globally quasi-uniform meshes

Mathematics of Computation
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis
Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates

Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes

SIAM Journal on Numerical Analysis
L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems

Journal of Scientific Computing
Short Note: An explicit expression for the penalty parameter of the interior penalty method

Journal of Computational Physics
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation

SIAM Journal on Numerical Analysis
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

Journal of Computational and Applied Mathematics
Discontinuous Galerkin Methods: Theory, Computation and Applications

Discontinuous Galerkin Methods: Theory, Computation and Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider some (anisotropic and piecewise constant) diffusion problems in domains of R^2, approximated by a discontinuous Galerkin method with polynomials of any fixed degree. We propose an a posteriori error estimator based on gradient recovery by averaging. It is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability. The lower bound is also established. Moreover these additional terms are negligible when the recovered gradient is superconvergent. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests.