A Fully Discrete Stabilized Finite Element Formulation For Non-Stationary Stokes Equation

In chapter1, the paper briefly introduces the development process of stabilized finite element method and some basic knowledge used in this paper.In chapter2, A fully discrete stabilized finite element method is studied and ana-lyzed for the two-dimensional non-stationary Stokes equation. The backward Euler semi-discrete formulation in time for non-stationary Stokes equation is established firstly. And then a fully discrete stabilized finite element formulation based on two local Gauss in-tegrals for non-stationary Stokes equation is directly established from time semi-discrete formulation. The spatial discretization is based on the P1—P1triangular element for the approximation of the velocity and pressure. And the error estimates for the fully discrete finite element approximate solutions are derived. The approaches studied here could make theoretical proof simpler and more convenient. And it can be viewed as a novel pathway for non-stationary Stokes equations.