The aim of this work is to show an abstract framework analyze the numerical approximation for a family linear degenerate parabolic mixed equations by using finite element method in space and Backward-Euler scheme time. We consider sufficient conditions prove that fully-discrete problem has unique solution quasi-optimal error estimates approximation. Furthermore, we formulations arising from dyn...

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

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...

Convergence of mixed finite element approximations to the Stokes problem in the primitive variables is examined in maximum norm. Quasioptimal pointwise error estimates are derived for discrete spaces satisfying a weighted inf-sup condition similar to the Babuska -Brezzi condition. The usual techniques employed to prove the inf-sup condition in energy norm can be easily extended to the present s...