Numerical Simulation Of Two Kinds Of Evolution Equations

In this paper , we consider several neumrical methods for the initial-boundary value problems of Sobolev equations and purely longtudinal motion equations of a homogeneous bar, obtain the error estimates of the discrete schemes for the two kinds of problems.In Chapter one,we consider the Expanded Mixed finite element methods for the Sobolev equationsThis method expands the standard mixed formulation in the sense that three variable are explixitly treatedithe scalar unknwon, its gradient and its flux. Based on this fomulation,expanded mixed finite element approximations of the Sobolev equations are considered.Optimal order error estimates for the scalar unknwon, its gradient and its flux in L2-norms are obtained for this new mixed formulation.Also, Quasi-optimal order estimates are obtained for the approximations of the the scalar unknwon.In Chapter two, we consider the finite element methods for the following initial-value problem of purely longtudinal motion of a homogeneous barIn this chapter,we give the error analysis of this discrete schemes and get op timal error estimates for the discrete solution of u.