Year: 2024
Author: Yanli Chen, Tie Zhang, Ying Sheng
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 860–877
Abstract
We present a primal-dual discontinuous Galerkin finite element method for a type of ill-posed elliptic Cauchy problem. It is shown that the discrete problem attains a unique solution, if the solution of the ill-posed elliptic Cauchy problems is unique. An optimal error estimate is obtained in a $H^1$-like norm. Numerical experiments are provided to demonstrate the efficiency of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0108
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 860–877
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: The ill-posed elliptic problem discontinuous Galerkin method primal-dual scheme optimal error estimate.