Moving Mesh Discontinuous Galerkin Methods for PDEs with Traveling Waves
For computational scientists solving PDEs with traveling waves, this method offers an efficient approach to resolve sharp fronts, though it is an incremental extension of existing moving mesh and dG techniques.
The paper develops a moving mesh discontinuous Galerkin method for nonlinear PDEs with traveling waves, demonstrating accurate resolution of sharp wave fronts and speeds for Burgers', Burgers'-Fisher, and Schlögl equations.
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the efficiency of the proposed moving mesh dG method for solving Burgers', Burgers'-Fisher and Schlögl(Nagumo) equations.