Numerical Simulation For Two Kinds Of Quasi-Linear Evolution Equations

In this paper,we consider the H1-Galerkin mixed finite element method for the nonlinear quasi-hyperbolic equation and mixed volume element method for the nonlinear pseudo-parabolic equation,and obtain the error estimates of this two discrete solutions.In chapter one,we consider the nonlinear quasi-hyperbolic equation which is simulated by H1-Galerkin mixed finite element method.This method first split the initial problem into a first order system and then propose a nonsymmetric version of a least square method that is an H1-Galerkin procedure for the approximating finite dimensional subspace can be relaxed for the proposed method.Moreover, the approxi-mating finite element space Vh and Wh are allowed to be of differing polynomial degrees. Hence,estimates have been obtained which distinguish the better approximating proper-ties of Vh and Wh.We obtain the optimal order of convergence theoretically.In chapter two,we consider the mixed volume method for the following nonlinear pseudo-parabolic equation We give the mixed volume scheme for the nonlinear pseudo-parabolic equation,and prove the mixed volume elleptic projection of the existence and uniqueness of the solution.L2 norm estimate about the ture solution and the discrete solution are obtained for the scheme.