Numerical Simulation For Two-dimensional PME By LDG Finite Element Method

In this paper, we will consider the simulation of the local discontinuous Galerkin (LDG) finite element method for the porous medium equation(PME). The main content is to construct a nonnegativity preserving limiter, which satisfies the physical nature of the PME. Here, two nonnegativity preserving limiters are presented. One limiter pro-posed for rectangular grids is essentially designed for linear cell approximations (P1), the other one is constructed for piecewise bilinear polynomials (Q1). And make some comparison of two methods. Finally, numerical results are given to show that the LDG method for the simulation of the PME is succeed to capture sharp interfaces without oscillation and also can get some interesting phenomena.