A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the finite element boundaries. When discontinuities are present, we locally apply dissipation around t...

We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time discretization method and with a spatial discretization based on adaptive discontinuous finite elements. The resulting method has full second order accuracy in ...

We present a new time discretization scheme based on the continuous Galerkin Petrov method of polynomial order 3 (cGP(3)-method) which is combined with a reduced numerical time integration (3-point Gauß-Lobatto formula). The solution of the new approach can be computed from the solution of the lower order cGP(2)-method, which requires to solve a coupled 2 × 2 block system on each time interval,...

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

In this piece of work using only three grid points, we propose two sets of numerical methods in a coupled manner for the solution of fourth-order ordinary differential equation u x f x, u x , u′ x , u′′ x , u′′′ x , a < x < b, subject to boundary conditions u a A0, u′ a A1, u b B0, and u′ b B1, where A0, A1, B0, and B1 are real constants. We do not require to discretize the boundary conditions....

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

For second harmonic generation in two-dimensional wave-guiding structures composed of segments that are invariant in the longitudinal direction, we develop an efficient numerical method based on the Dirichlet-to-Neumann (DtN) maps of the segments and a marching scheme using two operators and two functions. A Chebyshev collocation method is used to discretize the longitudinal variable for comput...

A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical...

To avoid the order reduction when third order implicit-explicit Runge-Kutta time discretization is used together with the local discontinuous Galerkin (LDG) spatial discretization, for solving convection-diffusion problems with time-dependent Dirichlet boundary conditions, we propose a strategy of boundary treatment at each intermediate stage in this paper. The proposed strategy can achieve opt...

Problem statement: Handling numerical data stored in a relational database has been performed differently from handling those numerical data stored in a single table due to the multiple occurrences (one-to-many association) of an individual record in the non-target table and non-determinate relations between tables. Numbers in Multi-Relational Data Mining (MRDM) were often discretized, after co...