Universität zu Köln

Klingenberg, Christian, Schnucke, Gero and Xia, Yinhua ORCID: 0000-0001-8120-3560 (2017). An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations. J. Sci. Comput., 73 (2-3). S. 906 - 943. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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Abstract

In this paper, an arbitrary Lagrangian-Eulerian local discontinuous Galerkin (ALE-LDG) method for Hamilton-Jacobi equations will be developed, analyzed and numerically tested. This method is based on the time-dependent approximation space defined on the moving mesh. A priori error estimates will be stated with respect to the -norm. In particular, the optimal () convergence in one dimension and the suboptimal () convergence in two dimensions will be proven for the semi-discrete method, when a local Lax-Friedrichs flux and piecewise polynomials of degree k on the reference cell are used. Furthermore, the validity of the geometric conservation law will be proven for the fully-discrete method. Also, the link between the piecewise constant ALE-LDG method and the monotone scheme, which converges to the unique viscosity solution, will be shown. The capability of the method will be demonstrated by a variety of one and two dimensional numerical examples with convex and noneconvex Hamiltonian.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klingenberg, Christian UNSPECIFIED UNSPECIFIED UNSPECIFIED Schnucke, Gero UNSPECIFIED UNSPECIFIED UNSPECIFIED Xia, Yinhua UNSPECIFIED orcid.org/0000-0001-8120-3560 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-210744
DOI:	10.1007/s10915-017-0471-2
Journal or Publication Title:	J. Sci. Comput.
Volume:	73
Number:	2-3
Page Range:	S. 906 - 943
Date:	2017
Publisher:	SPRINGER/PLENUM PUBLISHERS
Place of Publication:	NEW YORK
ISSN:	1573-7691
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FINITE-ELEMENT-METHOD; SCHEMES; DOMAINS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21074