Abstract In this paper, a new strategy for sub-element-based shock capturing discontinuous Galerkin (DG) approximations is presented. The idea to interpret DG element as collection of data and construct hierarchy low-to-high-order discretizations on set data, including first-order finite volume scheme up the full-order scheme. different are then blended according sub-element troubled cell indic...

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that pr...

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...

In this report, after pedagogical mathematical insight into basic notions of numerical analysis for di erential equations, more speci c Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wavepropagation problem. Stability analysis of the resulting sche...

In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling cond...

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on gener...

AdeR-AdeS is a two-component regulatory system, which controls expression of the adeABC efflux pump involved in Acinetobacter baumannii multidrug resistance. AdeR is a response regulator consisting of an N-terminal receiver domain and a C-terminal DNA-binding-domain. AdeR binds to a direct-repeat DNA in the intercistronic region between adeR and adeABC. We demonstrate a markedly high affinity b...

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization...

In this paper, we propose a local discontinuous Galerkin (LDG) method for nonlinear and possibly degenerate parabolic stochastic partial differential equations, which is high-order numerical scheme. It extends the (DG) purely hyperbolic equations to shares with DG its advantage flexibility. We prove L 2 -stability of scheme fully equations. Optimal error estimates ( O h (k+1) )) smooth solution...