Flux reconstruction for the \(P2\) nonconforming finite element method with application to a posteriori error estimation
type: Item
instance of: scholarly article
title: Flux reconstruction for the \(P2\) nonconforming finite element method with application to a posteriori error estimation
zbMATH Open document ID: 1266.65194
author: Kwang-Yeon Kim
published in: Applied Numerical Mathematics
publication date: 2012-11-12T00:00:00Z
review text: Two \(H(\text{div},\Omega)\)-conforming flux reconstruction approaches for the \(P2\) nonconforming finite element method are presented. The reconstruction methods are introduced by considering a standard elliptic boundary value problem of second order. In the second part, the results are extended to the Stokes problem. Two different local (element-by-element) approaches are discussed, which lead to flux reconstructions in first-order Raviart-Thomas, respectively, Brezzi-Douglas-Marini spaces. Both alternatives are then applied to a posteriori error estimation. Some numerical experiments for the Poisson equation, respectively, the Stokes problem illustrate the performance of the newly introduced methods.
reviewed by: Martin Reißel
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6104868
zbMATH Keywords: \(P2\) nonconforming finite element method
zbMATH Keywords: flux reconstruction
zbMATH Keywords: a posteriori error estimation
zbMATH Keywords: Raviart-Thomas space
zbMATH Keywords: elliptic boundary value problem
zbMATH Keywords: Stokes problem
zbMATH Keywords: Brezzi-Douglas-Marini spaces
zbMATH Keywords: numerical experiments
zbMATH Keywords: Poisson equation
MaRDI profile type: Publication
full work available at URL: j.apnum.2012.06.027
OpenAlex ID: W1987105533
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DOI: 10.1016/J.APNUM.2012.06.027
description: scientific article; zbMATH DE number 6104868