The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the m...

We analyze and compare different techniques to set up the stiffness matrix in the hp-version of the finite element method. The emphasis is on methods for second order elliptic problems posed on meshes including triangular and tetrahedral elements. The polynomial degree may be variable. We present a generalization of the Spectral Galerkin Algorithm of [7], where the shape functions are adapted t...

sedimentation is one of the most important problems in harbors that results in considerable economic costs. harbor planforms affects the flow pattern in the harbor basin and consequently, plays an important role in sediment transport and sedimentation. in the present study, a two dimensional depth-averaged hydrodynamic and sediment transport model has been developed to investigate the effect of...

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

In this paper, we present a numerical scheme for the propagation of acoustic waves in a heterogeneous medium in the context of the finite volume evolution Galerkin (FVEG) method (M. Lukáčová-Medvid’ová et al. J. Comput. Phys., 183:533–562, 2002). As a mathematical model we consider a wave equation system with space dependent wave-speed and impedance, which is used to study the wave propagation ...

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geoele...

Multigrid schemes for high order finite difference methods on summationby-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserv...

To simulate the rapid transient streamer discharge process, a method with high resolution and high order accuracy is usually required. This paper presents such a method based on discontinuous Galerkin (DG) method combined with hierarchical reconstruction (HR) for simulating the fluid model of streamer discharges. Numerical comparisons suggest that DG with HR is superior in both resolution and a...