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 ...

Hybridization between a method of moments called WCIP (Wave Concept Iterative Procedure) and volumic methods like the FDTLM (Frequency Domain Transmission Line Method), the FEM (Finite Element Method) and the HDG (Hybridizable Discontinuous Galerkin) method is presented in 2d in this paper. The considered problem is the Helmholtz equation in the frequency domain. Two test cases are provided to ...

In this talk we discuss the problem of constructing effective high order methods for the numerical solution of hyperbolic systems of balance laws, in presence of stiff source. Because of the stiffness, the use of implicit integrators is advisable, so that no restrictions on the time step due to small relaxation time will appear. Two different relaxation systems will be considered, namely hyperb...

Abstract. We present a general error estimation framework for a finite volume element (FVE) method based on linear polynomials for solving second-order elliptic boundary value problems. This framework treats the FVE method as a perturbation of the Galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of FVE methods. I...

We consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite e...

The subject of the paper is the analysis of three new evolution Galerkin schemes for a system of hyperbolic equations, and particularly for the wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following: the initial function is evolved us...

For the initial value problem of scalar conservation laws, a bound-preserving property is desired for numerical schemes in many applications. Traditional methods to enforce a discrete maximum principle by defining the extrema as those of grid point values in finite difference schemes or cell averages in finite volume schemes usually result in an accuracy degeneracy to second order around smooth...

We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the penalty parameter tends to infinity. We apply this result to equations of non-negative characteristic form and the non-linear, time dependent system of incompressible miscible displacement. Moreover, we investigate varyi...

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and th...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...