A numerical approach to solving an inverse parabolic problem using finite differential method

Abstract

Runge-Kutta discontinuous Galerkin (RKDG) \ufb01nite element method for hyperbolic conservation laws is a high order method, which can handle complicated geometries \ufb02exibly and treat boundary conditions easily. In this paper, we propose a new numerical method for treating interface using the advantages of RKDG \ufb01nite element method. We use level set method to track the moving interface. In every time step, a Riemann problem at the interface is de\ufb01ned. 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 \ufb02ow variables of the cell crossed are modi\ufb01ed through linear interpolation. Othewise, we do nothing.