Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation

Authors:
Kwang-Yeon Kim
Affiliations:
Department of Mathematics, Kangwon National University, Chuncheon 200-701, South Korea
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 9
Cited 1

Error estimators for nonconforming finite element approximations of the Stokes problem

Mathematics of Computation
Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

Mathematics of Computation
A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes

SIAM Journal on Numerical Analysis
Locally Conservative Fluxes for the Continuous Galerkin Method

SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation

SIAM Journal on Numerical Analysis
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods

Numerische Mathematik
Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements

SIAM Journal on Numerical Analysis
A framework for obtaining guaranteed error bounds for finite element approximations

Journal of Computational and Applied Mathematics

Fully computable a posteriori error estimates for the Stokes equation without the global inf-sup constant

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this work we propose a new and simple way of reconstructing H(div,@W)-conforming flux approximations for the P2 nonconforming finite element method of second order elliptic problems which fulfill the local mass conservation and optimal a priori error estimates. This reconstruction is crucially used in deriving an a posteriori error estimator which gives a guaranteed upper bound on the actual error. We also apply the same technique to the Stokes problem in order to reconstruct a H(div,@W)-conforming pseudo-tensor approximation which are then used for a posteriori error estimation. Some numerical results are presented to illustrate the performance of the error estimators thus obtained.