A new primal-dual weak Galerkin finite element method for ill-posed elliptic Cauchy problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Wang, Chunmei¹ 

[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

关键词: Primal-dual;    Weak Galerkin;    Finite element methods;    Elliptic Cauchy problem;    Weak gradient;    Polygonal or polyhedral meshes;   

DOI  :  10.1016/j.cam.2019.112629

来源: Elsevier

【 摘 要 】

A new numerical method is devised and analyzed for a type of ill-posed elliptic Cauchy problems by using the primal-dual weak Galerkin finite element method. This new primal-dual weak Galerkin algorithm is robust and efficient in the sense that the system arising from the scheme is symmetric, well-posed, and is satisfied by the exact solution (if it exists). An error estimate of optimal order is established for the corresponding numerical solutions in a scaled residual norm. In addition, a mathematical convergence is established in a weak L-2 topology for the new numerical method. Numerical results are reported to demonstrate the efficiency of the primal-dual weak Galerkin method as well as the accuracy of the numerical approximations. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free