TY - JOUR
T1 - A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 475
EP - 495
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.m1331
UR - https://global-sci.org/intro/article_detail/nmtma/12419.html
KW - 
AB - <p style="text-align: justify;">In this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. Extensive numerical experiments illustrate the feasibility of the method.</p>