The SGBEM-FEM alternating method suitable for the solution of elastic and elasticplastic three-dimensional fracture mechanics problems is presented. The crack is modeled by the symmetric Galerkin boundary element method (SGBEM), as a distribution of displacement discontinuities in an infinite medium. The finite element method (FEM) is used for stress analysis of the uncracked finite body. The s...

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is developed. It is based on [H 0 (Ω)] -conforming velocity reconstruction and H(div, Ω)-conforming, locally conservative flux (stress) reconstruction. It gives guaranteed, fully computable global upper bounds as well as local lower bounds on the energy error. In order to apply this framework to a given ...

We present hybrid finite element methods, which are equivalent to a discontinuous Galerkin method based on the ultra weak variational formulation (UWVF) by Cessenat and Despres. When solving a scalar or vectorial wave equation with hybrid finite elements, normal and tangential continuity of the flux field, respectively, is broken across element interfaces and reinforced again by introducing hyb...

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP) onto correction procedure via reconstruction (CPR). MLP, which has been originally developed in finite volume method (FVM), provides an accurate, robust and efficient oscillation-control mechanism in multiple dimensions for linear reconstruction. Recently, MLP has been extended into higher-ord...

Finite volume moving mesh methods are developed for unsteady one-dimensional partial diierential equations. The methods can be viewed as conservative discretisations of the Lagrangian form of the original diier-ential equations. Grid points are moved using the idea of mesh equidistri-bution. The coupled unsteady diierential equations and grid movement equations are solved using a robust and eec...

In this report, we address several aspects of the approximation of the MHD equations by a Galerkin Discontinuous finite volume schemes. This work has been initiated during a CEMRACS project in July and August 2008 in Luminy. The project was entitled GADMHD (for GAlerkin Discontinuous approximation for the Magneto-Hydro-Dynamics). It has been supported by the INRIA CALVI project. 1 Some properti...

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy [10]. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes [6] also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations...

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations wit...

In this paper, we present a class of finite volume trigonometric weighted essentially non-oscillatory (TWENO) schemes and use them as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods based on trigonometric polynomial spaces to solve hyperbolic conservation laws and highly oscillatory problems. As usual, the goal is to obtain a robust and high order limiting procedure for such a RK...

In [20], Qiu and Shu investigated using weighted essentially non-oscillatory (WENO) finite volume methodology as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods for solving nonlinear hyperbolic conservation law systems on structured meshes. In this continuation paper, we extend the method to solve two dimensional problems on unstructured meshes, with the goal of obtaining a r...