@Article{JICS-3-215, author = {}, title = {A numerical approach to solving an inverse parabolic problem using finite differential method}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {3}, number = {3}, pages = {215--224}, abstract = {Runge-Kutta discontinuous Galerkin (RKDG) finite element method for hyperbolic conservation laws is a high order method, which can handle complicated geometries flexibly and treat boundary conditions easily. In this paper, we propose a new numerical method for treating interface using the advantages of RKDG finite element method. We use level set method to track the moving interface. In every time step, a Riemann problem at the interface is defined. The two cells adjacent to the interface are computed using the Riemann problem solver. If the interface crosses a cell in the next time step, the values of the flow variables of the cell crossed are modified through linear interpolation. Othewise, we do nothing. }, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22770.html} }