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Volume 16, Issue 4
A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems

Yanli Chen, Tie Zhang & Ying Sheng

DOI: 10.4208/aamm.OA-2022-0108

Adv. Appl. Math. Mech., 16 (2024), pp. 860-877.

Published online: 2024-05

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  • 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.

  • Keywords

The ill-posed elliptic problem, discontinuous Galerkin method, primal-dual scheme, optimal error estimate.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-860, author = {Chen , YanliZhang , Tie and Sheng , Ying}, title = {A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0108}, url = {http://global-sci.org/intro/article_detail/aamm/23114.html} }
TY - JOUR T1 - A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems AU - Chen , Yanli AU - Zhang , Tie AU - Sheng , Ying JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 860 EP - 877 PY - 2024 DA - 2024/05 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2022-0108 UR - https://global-sci.org/intro/article_detail/aamm/23114.html KW - The ill-posed elliptic problem, discontinuous Galerkin method, primal-dual scheme, optimal error estimate. AB -

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.

Chen , YanliZhang , Tie and Sheng , Ying. (2024). A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems. Advances in Applied Mathematics and Mechanics. 16 (4). 860-877. doi:10.4208/aamm.OA-2022-0108
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