Adapive discontinuous galerkin method for one-dimensional shallow water equations

The Discontinuous Galerkin (DG) method for solving the one-dimensional advection equation and shallow water equations are presented in this thesis. To improve the efficiency of this method, two types of adaptive technique are employed. These are the adaptive polynomial (p-adaptive) and the adaptive mesh (h-adaptive). The main purpose is to improve the accuracy of numerical solution during time integration process. Troubled cells needed to be refined are detected by two types of indicators, which are error and gradient indicators. The present schemes have been applied for solving the advection equation and the standard shallow water equations for both wet bed and dry bed. The moving shock can be detected correctly by the adaptive mesh criteria when the HLL flux approximation is employed at the interface of cell volume.