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.

Abstract. In this paper, a bilinear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection – diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter ǫ provided only that ǫ ≤ N. An O(N(lnN)) convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumpti...

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.

we derive error estimates in the appropriate norms, for the streamlinediffusion (sd) finite element methods for steady state, energy dependent,fermi equation in three space dimensions. these estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.high order sd method together with implicit integration are used. the formulationis strongly consistent...