TY - JOUR
T1 - An Improved Non-Traditional Finite Element Formulation for Solving the Elliptic Interface Problems
JO - Journal of Computational Mathematics
VL - 1
SP - 39
EP - 57
PY - 2014
DA - 2014/02
SN - 32
DO - http://doi.org/10.4208/jcm.1309-m4207
UR - https://global-sci.org/intro/article_detail/jcm/9868.html
KW - Elliptic equation, Sharp-edged interface, Jump condition, Matrix coefficient.
AB - <p style="text-align: justify;">We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid are considered. Both Dirichlet and Neumann boundary conditions are discussed. The coefficient matrix data can be given only on the grids, rather than an analytical function. Extensive numerical experiments show that this method is second order accurate in the $L^∞$ norm.</p>