Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials

Abstract

In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-alpha method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatial discretization. We also discuss the effect of higher polynomial orders on the convergence rates, focusing on the nonlinear DSW problem. Our numerical experiments show that optional convergence rates can be obtained for polynomial orders 1 through 4.