An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations

作者：Klingenberg, Christian; Schnucke, Gero; Xia, Yinhua^*

来源：Journal of Scientific Computing, 2017, 73(2-3): 906-942.

DOI：10.1007/s10915-017-0471-2

• Arbitrary Lagrangian-Eulerian method
• Local discontinuous Galerkin method
• Hamilton-Jacobi equations
• Geometric conservation law
• Error estimates

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.

• 出版日期2017-12
• 单位中国科学技术大学