In this paper, a predictor-corrector finite difference-streamline diffusion finite element scheme is constructed for time-dependent quasilinear convection-diffusion problem. For the scheme considered, the solvility is proved, and the error estimate in L(L2)-norm is established. It has 2-order accuracy in time direction and quasi-optimal order accuracy in space variables.
In this paper, the economical finite difference-streamline diffusion (EFDSD) schemes based on the linear F.E. space for time-dependent linear and non-linear convection-dominated diffusion problems are constructed. The stability and error estimation with quasi-optimal order approximation are established in the norm stronger than L^2 - norm for the schemes considered. It is indicated by the results obtained that,for linear F.E. space, the EFDSD schemes have the same specific properties of stability and convergence as the traditional FDSD schemes for the problems discussed.
In this paper, a new finite element method, discontinuous-streamline diffusion method, is studied for first-order linear hyperbolic equation. A discontinuity-type explicit finite element scheme with artificial diffusion parameter is constructed, the stability and optimal rate of convergence in proper norm are established for the considered scheme. Finally, a numerical example is provided to show the highly efficiency of the now scheme.
In this paper, two kinds of Finite Volume-Streamline Diffusion Finite Element methods (FV-SD) for steady convection dominated-diffusion problem are presented and the stability and error estimation for the numerical schemes considered are established in the norm stronger than L^2-norm. The theocratical analysis and numerical example show that the schemes constructed in this paper are keeping the basic properties of Streamline Diffusion (SD) method and they are more economical in computing scale than SD scheme, and also, they have same accuracy as FV-Galerkin FE method and better stability than it.
