Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method

Authors:
Qiang Zhang;Zi-Long Wu
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, People's Republic of China 210093;School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, People's Republic of China 050031
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

In this paper we will consider the simulation of the local discontinuous Galerkin (LDG) finite element method for the porous medium equation (PME), where we present an additional nonnegativity preserving limiter to satisfy the physical nature of the PME. We also prove for the discontinuous 驴0 finite element that the average in each cell of the LDG solution for the PME maintains nonnegativity if the initial solution is nonnegative within some restriction for the flux's parameter. Finally, numerical results are given to show the advantage of the LDG method for the simulation of the PME, in its capability to capture accurately sharp interfaces without oscillation.