4.7 Article

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

期刊

JOURNAL OF COMPUTATIONAL PHYSICS
卷 334, 期 -, 页码 102-124

出版社

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.12.031

关键词

Transport equation; Advection remap; Flux corrected transport; Bernstein basis finite elements; Maximum principle; High-order discontinuous finite elements

资金

  1. U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344, LLNL-JRNL-684083]
  2. German Research Association (DFG) [KU 1530/15-1]

向作者/读者索取更多资源

In this work we present aFCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported. (C) 2016 Elsevier Inc. All rights reserved.

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