期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 38, 期 2, 页码 127-148出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-008-9223-7
关键词
Local discontinuous Galerkin; Finite element; Porous medium equation; Nonnegativity preserving limiter
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 a(TM)(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.
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