Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
500034 | Computer Methods in Applied Mechanics and Engineering | 2006 | 15 Pages |
In this paper, we discuss the development, verification, and application of an hp discontinuous Galerkin (DG) finite element model for solving the shallow water equations (SWE) on unstructured triangular grids. The h and p convergence properties of the method are demonstrated for both linear and highly nonlinear problems with advection dominance. Standard h-refinement for a fixed p leads to p + 1 convergence rates, while exponential convergence is observed for p-refinement for a fixed h. It is also demonstrated that the use of p-refinement is more efficient for problems exhibiting smooth solutions. Additionally, the ability of p-refinement to adequately resolve complex, two-dimensional flow structures is demonstrated in the context of a coastal inlet problem.