A maximum-principle preserving finite element method for scalar conservation equations
A maximum-principle preserving finite element method for scalar conservation equations
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DOI：
10.1016/j.cma.2013.12.015
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发表时间：
2014-04
影响因子：
7.2
通讯作者：
J. Guermond;Murtazo Nazarov
中科院分区：
文献类型：
--
作者：
J. Guermond;Murtazo Nazarov
本文介绍了一种一阶粘性方法，在任意空间维的任意网格上使用连续有限元显式逼近具有Lipschitz通量的标量守恒方程。在集中质量矩阵正定的条件下，证明了该方法在通常CFL条件下满足局部极大值原理。该方法与单元类型无关;例如，网格可以是三个空间维度中的四面体、六面体和棱柱的组合。
This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions.