Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems
Year: 2022
Author: Chunmei Wang
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 33–51
Abstract
A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20348
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 33–51
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Primal-dual finite element method weak Galerkin low regularity elliptic Cauchy equations ill-posed.