期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 79, 期 3, 页码 746-763出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.07.031
关键词
Primal-dual weak Galerkin; Finite element methods; Elliptic Cauchy problem
资金
- National Science Foundation, USA [DMS-1849483]
- National Science Foundation, USA IR/D program
The authors propose and analyze a well-posed numerical scheme for a type of ill-posed elliptic Cauchy problem by using a constrained minimization approach combined with the weak Galerkin finite element method. The resulting Euler-Lagrange formulation yields a system of equations involving the original equation for the primal variable and its adjoint for the dual variable, and is thus an example of the primal-dual weak Galerkin finite element method. This new primal-dual weak Galerkin algorithm is consistent in the sense that the system is symmetric, well-posed, and is satisfied by the exact solution. A certain stability and error estimates were derived in discrete Sobolev norms, including one in a weak L-2 topology. Some numerical results are reported to illustrate and validate the theory developed in the paper. (C) 2019 Elsevier Ltd. All rights reserved.
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