Numerical Simulation Of The Mixed Finite Element Method For Two Kinds Of Evolution Equations

The purpose of the paper is to investigate the convergence of the mixed finite element method for initial-boundary for the pseudoparabolic intergo-differrential equation and the convection-dominated transport problems.In Chaper one ,we consider the mixed finite element method for the following problemBased on the Raviart-Thoams space Vh× Wh (?) H(div;Ω) × L2(Ω), optimal order estimates are odt.ained for the approximation of u, ut,the associated velocity p and divp respectively in L∞(L2).L∞(L2),L∞(L2)2.L∞(L2). Quasi-optimal order estimates are obtained for the approximations of u,ut in L∞(L∞) and p in L∞(L∞)2.Numerical example shows that the method we propose is effective.In Chapter two,we consider the Expanded Mixed finite element methods for the pseudoparabolic intergo-differrential equationThis method expands the standard mixed formulation in the sense that three variableare explixitly treated:the scalar unknwon, its gradient and its flux. Based on this fo-mulation,expanded mixed finite element approximations of the pseudoparabolic intergo-differrential equations are considered.Optimal order error estimates for the scalar unkn-...