A well-balanced element-free Galerkin method for the nonlinear shallow water equations

In this paper, we consider the nonlinear shallow water equations over variable bottom topography in one dimension and propose a well-balanced element-free Galerkin method for solving this system. The proposed scheme has the features of being high-order accurate for general solutions and exactly preserving the still-water stationary solution. The main ingredient to achieve the well-balanced property is to use a special decomposition to the source term and discretize the source term as the flux term. Numerical tests are presented to illustrate the accuracy and validity of the proposed scheme.