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.

引用

页数：18

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