A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for b...

We analyze a numerical algorithm for solving radiative transport equation with vacuum or reflection boundary condition that was proposed in [4] with angular discretization by finite element method and spatial discretization by discontinuous Galerkin or finite difference method.

In order to perform accurate electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, the so-called EEG forward problem. Therefore, it is necessary to apply numerical methods that are able to take the individual geometr...

The focus of this effort is to produce a two dimensional inviscid, compressible flow solver using the Discontinuous Galerkin Finite Element approach. The Discontinuous Galerkin method seeks to project the exact solution onto a finite polynomial space while allowing for discontinuities at cell interfaces. This allows for the natural discontinuity capture that is required for a compressible flow ...

1 This work was performed at Sandia National Laboratories, operated for the U.S. Department of Energy under contract #DE-AC04-76DP00789. 2 This work was partially supported by Sandia National Laboratories under Research Agreement #67-8709. 3 On Faculty Sabbatical to Sandia National Laboratories. Abstract We describe a fine-grained, element-based data migration system that dynamically maintains ...

We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which include the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, “mass” and energy are preserved. We discretize ...

This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly ...

In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated with the simulation of the elastic deformation of a wing in subsonic and transonic flow.

In order to solve the elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured meshes, a nodal Discontinuous Galerkin Finite Element Method (DG-FEM) is presented, which combines the geometrical flexibility of the Finite Element Method and strongly nonlinear wave simulation capability of the Finite Volume Method. The equations of nonlinear elastody...