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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu Province, 210093, People’s Republic of China

    Qiang Zhang

  2. School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, Hebei Province, 050031, People’s Republic of China

    Zi-Long Wu

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  1. Qiang Zhang
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  2. Zi-Long Wu
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Correspondence to Qiang Zhang.

Additional information

The research of Q. Zhang is supported by CNNSF grant 10301016.

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Zhang, Q., Wu, ZL. Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method. J Sci Comput 38, 127–148 (2009). https://doi.org/10.1007/s10915-008-9223-7

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  • DOI: https://doi.org/10.1007/s10915-008-9223-7

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