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

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

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.

Author Details

Yanli Chen

Tie Zhang

Ying Sheng