Paper Info
Title
An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations.
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 \(\mathrm {L}^{\infty }\left( 0,T;\mathrm {L}^{2}\left( \Omega \right) \right) \)-norm. In particular, the optimal (\(k+1\)) convergence in one dimension and the suboptimal (\(k+\frac{1}{2}\)) 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.
Year
DOI
Venue
2017
10.1007/s10915-017-0471-2
J. Sci. Comput.
Keywords
Field
DocType
Arbitrary Lagrangian–Eulerian method, Local discontinuous Galerkin method, Hamilton–Jacobi equations, Geometric conservation law, Error estimates
Discontinuous Galerkin method,Mathematical optimization,Polynomial,Hamiltonian (quantum mechanics),Mathematical analysis,Eulerian path,Viscosity solution,Conservation law,Monotone polygon,Mathematics,Piecewise
Journal
Volume
Issue
ISSN
73
2-3
0885-7474
Citations 
PageRank 
References 
0
0.34
10
Authors
3
Name
Order
Citations
PageRank
Christian Klingenberg1589.36
Gero Schnücke211.03
Yinhua Xia39710.49