The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown ...

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numer...

We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

This study is concerned with the solution of the time domain Maxwell’s equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of equations is solved using a centered flux discontinuous Galerkin formulation for the discretization in space and a second order ...

H(div) conforming and discontinuous Galerkin (DG) methods are designed for incompressible Euler’s equation in two and three dimension. Error estimates are proved for both the semi-discrete method and fully-discrete method using backward Euler time stepping. Numerical examples exhibiting the performance of the methods are given.

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous G...

This paper is concerned with the stability and convergence of fully discrete Galerkin methods for boundary integral equations on bounded piecewise smooth surfaces in R 3. Our theory covers equations with very general operators , provided the associated weak form is bounded and elliptic on H , for some 2 ?1; 1]. In contrast to other studies on this topic, we do not assume our meshes to be quasiu...

The main purpose of this paper is to develop a fast fully discrete Fourier– Galerkin method for solving the boundary integral equations reformulated from the modified Helmholtz equation with boundary conditions. We consider both the nonlinear and the Robin boundary conditions. To tackle the difficulties caused by the two types of boundary conditions, we provide an improved version of the Galerk...