in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

In this work, we design, analyze and test a local discontinuous Galerkin method for solving the Burgers–Poisson equation. This model, proposed by Whitham [Linear and Nonlinear Waves, John Wiley & Sons, New York, 1974] as a simplified model for shallow water waves, admits conservation of both momentum and energy as two invariants. The proposed numerical method is high order accurate and preserve...

Abstract. The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem in a Gelfand triple with the pivot space H. This allows to employ methods of the theory of monotone operators in order to study fully discrete approximations combining a Galerkin method (including conforming finite element methods) with the backward Euler scheme. Convergence is shown eve...

We present a class of chemical reactor systems, modeled numerically using a fractional multistep method between the reacting and diffusing modes of the system, subsequently allowing one to utilize algebraic techniques for the resulting reactive subsystems. A mixed form discontinuous Galerkin method is presented with implicit and explicit (IMEX) timestepping strategies coupled to dioristic entro...

In this paper, we apply the local discontinuous Galerkin (LDG) method to 2D Keller– Segel (KS) chemotaxis model. We improve the results upon (Y. Epshteyn and A. Kurganov, SIAM Journal on Numerical Analysis, 47 (2008), 368-408) and give optimal rate of convergence under special finite element spaces. Moreover, to construct physically relevant numerical approximations, we develop a positivity-pre...

We consider a class of consistently ordered matrices which arise from the discretization of Boundary Value Problems (BVPs) when the finite element collocation method, with Hermite elements, is used. Through a recently derived equivalence relationship for the asymptotic rates of convergence of the Modified Successive Overrelaxation (MSOR) and a certain 2-step iterative method, we determine the o...