A two-dimensional numerical model for the solution of nonlinear shallow water equations (NSWEs) using discontinuous Galerkin finite element method (DGFEM) is presented. new adaptation thin-film approach developed wetting/drying treatment. The applied to a number test cases that can be characterized as swash flows, or are particularly useful flow modeling. DGFEM shows robustness and provides acc...

In this paper we give an analysis of a bubble stabilized discontinuous Galerkin method (BSDG) for elliptic and parabolic problems. The method consists of stabilizing the numerical scheme by enriching the discontinuous finite element space elementwise by quadratic non-conforming bubbles. This approach leads to optimal convergence in the space and time discretization parameters. Moreover the dive...

The Runge–Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge–Kutta time discretizations, and limiters. In this paper, we investigate using the RKDG finite element method for compressible...