Numerical Simulation For Two Kinds Of Partial Differential Equations

In this paper, we consider the numerical simulation for two kinds of partial differential equations: one is the non-stationary Stokes equation and the other is the visco-elasticity equation.In Chapter one, we consider the non-stationary Stokes equationThe Stokes equation is transformed into its stream function-vorticity form, then the mixed finite element method is employed to approxiamate the stream function, the vorticity and the velocity of the fluid. Finally the optimal order L2-error estimates are obtained for the stream function, the vorticity and the velocity.In Chapter two, the generalized difference scheme is presented for the visco-elasticity equationThe optimal order Lp and W1,p-error estimates for u-uh and the superconvergence results for uh-Vhu are proved, where Vhu stands for the Ritz - Volterra projection of...