@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} }