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

• Published in: Applied numerical mathematics Vol. 62; no. 12; pp. 1701 - 1717
• Main Author: Kim, Kwang-Yeon
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2012
• Subjects: A posteriori error estimation; Flux reconstruction; P2 nonconforming finite element method; Flux reconstruction; A posteriori error estimation; P2 nonconforming finite element method
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2012.06.027

In this work we propose a new and simple way of reconstructing H(div,Ω)-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,Ω)-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.