Convergence of a characteristic-Galerkin scheme for a shallow water problem

A characteristic-Galerkin approximation to a system of shallow water equations

A Discontinuous Galerkin Global Shallow Water Model

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are app...

Convergence Analysis of a Quadrature Finite Element Galerkin Scheme for a Biharmonic Problem

A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...

Convergence of a Discontinuous Galerkin Scheme for the Neutron Transport

We study the spatial discretization for the numerical solution of a model problem for the neutron transport equation in an innnite cylindrical media. Based on using an interpolation technique in the discontinuous Galerkin nite element procedure, and regulariz-ing properties of the solution operator, we derive an optimal error estimate in L 2 ?norm for the scalar ux. This result, combined with a...

A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations

We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DGmethod for the depth-integrated shallow water equations. The method described here is an extension ...