An a posteriori error estimator for the weak Galerkin least-squares finite-element method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:362

Article; Proceedings Paper

Adler, James H.¹  Hu, Xiaozhe¹  Mu, Lin²  Ye, Xiu³ 

[1] Tufts Univ, Dept Math, Medford, MA 02155 USA

[2] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN 37831 USA

[3] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

关键词: Weak Galerkin;    Finite-element methods;    Least-squares finite-element methods;    Second-order elliptic problems;   

DOI  :  10.1016/j.cam.2018.09.049

来源: Elsevier

【 摘 要 】

In this paper, we derive an a posteriori error estimator for the weak Galerkin least squares (WG-LS) method applied to the reaction-diffusion equation. We show that this estimator is both reliable and efficient, allowing it to be used for adaptive refinement. Due to the flexibility of the WG-LS discretization, we are able to design a simple and straightforward refinement scheme that is applicable to any shape regular polygonal mesh. Finally, we present numerical experiments that confirm the effectiveness of the estimator, and demonstrate the robustness and efficiency of the proposed adaptive WG-LS approach. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free