A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems

被引：0
|
作者：
Chen, Yanli [1 ]
Zhang, Tie [1 ,2 ]
Sheng, Ying [1 ]
机构：
[1] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China
[2] Northeastern Univ, State Key Lab Synthet Automat Proc Ind, Shenyang 110004, Liaoning, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2024年
关键词：
The ill-posed elliptic problem; discontinuous Galerkin method; primal-dual scheme; optimal error estimate; QUASI-REVERSIBILITY; DATA ASSIMILATION; INVERSE PROBLEMS; SOLVE; PART;
D O I：
10.4208/aamm.OA-2022-0108xxx2024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 H1-like norm. Numerical experiments are provided to demonstrate the efficiency of the proposed method.
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页数：18
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