We present a generalization of the finite volume evolution Galerkin scheme [17, 18] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex...

A constitutive model based on two–dimensional unstructured Galerkin finite volume method (GFVM) is introduced and applied for analyzing nonlinear behavior of cracked concrete structures in equilibrium condition. The developed iterative solver treats concrete as an orthotropic nonlinear material and considers the softening and hardening behavior of concrete under compression and tension by using...

We study a very simple model for nucleation-and-growth in infinite volume in the low-temperature limit. Despite its simplicity, this model exhibits a very rich metastable behavior. Depending on the speed of growth, the system goes trough four different regimes: 1) both the “shape of the critical droplet” and the typical relaxation time are the same as in finite volume. 2) the “shape of the crit...

In this paper we analyze the combine influence of radiation and dissipation on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular cavity using Darcy model. Making use of the incompressibility the governing non-linear coupled equations for the momentum, energy and diffusion are derived in terms of the non-dimensional stream function, temperatur...

Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accur...

Abstract. We introduce a stochastic Galerkin mixed formulation of the steady-state diffusion equation and focus on the efficient iterative solution of the saddle-point systems obtained by combining standard finite element discretisations with two distinct types of stochastic basis functions. So-called mean-based preconditioners, based on fast solvers for scalar diffusion problems, are introduce...

This work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single-phase fluid. The equations of motion, formulated in the space-frequency domain, include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high-freque...

In order to perform 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, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the indiv...

In this paper, a fully discrete stabilized discontinuous Galerkin method is proposed to solve the Biot's consolidation problem. The existence and uniqueness of the finite element solution are obtained. The stability of the fully discrete solution is discussed. The corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained. The error es...