NDLI: A new theoretically motivated higher order upwind scheme on unstructured grids of simplices

Content Provider	Springer Nature Link
Author	Wierse, Monika
Copyright Year	1997
Abstract	Many approaches exist to define a cell-centered upwind finite volume scheme of higher order on an unstructured grid of simplices. However, real theoretical motivation in the form of a convergence result does not exist for these approaches. Furthermore, some theoretical results of convergence exist for higher order finite volume methods, where no description of the numerical implementation is given to realize the necessary requirements for the convergence theory. Therefore we present in this paper a new limiter function which is motivated by these requirements and ensures a convergent scheme in the theoretical context: The approximated solution converges to the entropy solution in the case of scalar conservation laws in two space dimensions. This new limiter function is combined with a typical class of reconstruction functions very efficiently, which is illustrated by several test examples for scalar conservation laws as well as systems of such laws. In connection with the requirements to be fulfilled, a proof of a maximum principle of the finite volume scheme applied to simplices and dual cells is given. So for the approach of the higher order upwind finite volume scheme on dual cells, as used in several papers, a missing proof is now given. The ideas in this proof are also applied to the discontinuous Galerkin method, so that an existing maximum principle can be improved considerably. The main advantage comes from the fact that no requirements on the discretization of the domain are necessary: no B-triangulations or Delaunay triangulation are needed.
Starting Page	303
Ending Page	335
Page Count	33
File Format	PDF
ISSN	10197168
Journal	Advances in Computational Mathematics
Volume Number	7
Issue Number	3
e-ISSN	15729044
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1997-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Numeric Computing Mathematics Algebra Calculus of Variations and Optimal Control Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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