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 - <p style="text-align: justify;">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.</p>