Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method |
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Authors: | Qiang Zhang Zi-Long Wu |
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Affiliation: | (1) Department of Mathematics, Nanjing University, Nanjing, Jiangsu Province, 210093, People’s Republic of China;(2) School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, Hebei Province, 050031, People’s Republic of China |
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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 ℙ0 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.
The research of Q. Zhang is supported by CNNSF grant 10301016. |
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Keywords: | Local discontinuous Galerkin Finite element Porous medium equation Nonnegativity preserving limiter |
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