A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes

[摘要] In this paper, we present a posteriori error estimate of a new weak Galerkin (WG) finite element method for the second order elliptic interface problems. Instead of introducing the local weak derivatives on each element, the bilinear form is computed through the inner product of traditional defined derivatives. The proposed numerical scheme is symmetric and positive definite, and can be applied to polygonal meshes. In the a posteriori error estimate, we construct a error indicator that can be applied to polygonal meshes or meshes with hanging nodes. The reliability and efficiency of the designed error estimator have been proved in this work. Extensive numerical tests are performed to validate our algorithm. These results demonstrate the effectiveness of the adaptive mesh refinement guided by the proposed error estimator. (C) 2018 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-15

[效力级别]  Proceedings Paper

[关键词] Weak Galerkin;Finite element methods;Second-order elliptic interface problems;A priori error estimate;A posterior error estimate;Polygonal meshes