Paper Info
Title
Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension.
Abstract
In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method with a time-dependent approximation space for one dimensional conservation laws, which satisfies the geometric conservation law. For the semi-discrete ALE-DG method, when applied to nonlinear scalar conservation laws, a cell entropy inequality, L-2 stability and error estimates are proven. More precisely, we prove the sub-optimal (k + 1/2) convergence for monotone fluxes and optimal (k + 1) convergence for an upwind flux when a piecewise P-k polynomial approximation space is used. For the fully-discrete ALE-DG method, the geometric conservation law and the local maximum principle are proven. Moreover, we state conditions for slope limiters, which ensure total variation stability of the method. Numerical examples show the capability of the method.
Year
DOI
Venue
2017
10.1090/mcom/3126
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Arbitrary Lagrangian-Eulerian discontinuous Galerkin method,hyperbolic conservation laws,geometric conservation law,cell entropy inequality,error estimates,maximum principle,slope limiter conditions
Discontinuous Galerkin method,Mathematical optimization,Maximum principle,Nonlinear system,Polynomial,Mathematical analysis,Eulerian path,Conservation law,Monotone polygon,Piecewise,Mathematics
Journal
Volume
Issue
ISSN
86
305
0025-5718
Citations 
PageRank 
References 
1
0.37
6
Authors
3
Name
Order
Citations
PageRank
Christian Klingenberg1589.36
Gero Schnücke210.37
Yinhua Xia39710.49