TY - JOUR
T1 - L​ow Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems
AU - Wang , Chunmei
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 33
EP - 51
PY - 2022
DA - 2022/03
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/20348.html
KW - Primal-dual, finite element method, weak Galerkin, low regularity, elliptic Cauchy equations, ill-posed.
AB - <p style="text-align: justify;">A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.</p>