Robust Equilibrated Error Estimator for Diffusion Problems : Mixed Finite Elements in Two Dimensions
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 22 |
Number of pages | 22 |
Journal / Publication | Journal of Scientific Computing |
Volume | 83 |
Issue number | 1 |
Online published | 10 Apr 2020 |
Publication status | Published - Apr 2020 |
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Abstract
This paper introduces and analyzes an equilibrated a posteriori error estimator for mixed finite element approximations to the diffusion problem in two dimensions. The estimator, which is a generalization of those in Braess and Schöberl (Math Comput 77:651–672, 2008) and Cai and Zhang (SIAM J Numer Anal 50(1):151–170, 2012), is based on the Prager–Synge identity and on a local recovery of a gradient in the curl free subspace of the H (curl)-confirming finite element spaces. The resulting estimator admits guaranteed reliability, and its robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.
Citation Format(s)
Robust Equilibrated Error Estimator for Diffusion Problems : Mixed Finite Elements in Two Dimensions. / Cai, Difeng; Cai, Zhiqiang; Zhang, Shun.
In: Journal of Scientific Computing, Vol. 83, No. 1, 22, 04.2020.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review