TY - JOUR
T1 - A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients
AU - Wang , Liqun
AU - Hou , Songming
AU - Shi , Liwei
AU - Zhang , Ping
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 216
EP - 240
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0099
UR - https://global-sci.org/intro/article_detail/aamm/12929.html
KW - Petrov-Galerkin finite element method, jump condition, bilinear.
AB - <p style="text-align: justify;">In this paper, a bilinear Petrov-Galerkin finite element method is introduced to solve the variable matrix coefficient elliptic equation with interfaces using non-body-fitted grid. Different cases the interface cut the cell are discussed. The condition number of the large sparse linear system is studied. Numerical results demonstrate that the method is nearly second order accurate in the $L^\infty$ norm and $L^2$ norm, and is first order accurate in the $H^1$ norm.</p>