A symmetric weak Galerkin method for solving non-divergence form elliptic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:372

Article

Zhai, Qilong¹  Tian, Tian²  Zhang, Ran³  Zhang, Shangyou⁴ 

[1] Peking Univ, Dept Math, Changchun, Peoples R China

[2] Peking Univ, Dept Math, Beijing, Peoples R China

[3] Jilin Univ, Dept Math, Changchun, Peoples R China

[4] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

关键词: Weak Galerkin finite element method;    Triangular grid;    Elliptic equation;    Non-divergence form;   

DOI  :  10.1016/j.cam.2019.112693

来源: Elsevier

【 摘 要 】

We reformulate the second order non-divergence form elliptic equations in a symmetric variation form, i.e., a least-squares form. We design a weak Galerkin finite element method for this high-regularity formulation. The optimal order of convergence is proved. Numerical results verify the theory. In addition, numerical results, compared to the existing weak Galerkin method for the non-symmetric form, and the new methods show advantage on the accuracy and the degree of freedoms. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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