Application Of The Mixed Finite Element Method For Two Kinds Of Quasilinear

In this paper, we consider the mixed movolume method and mixed finite elementmethod for the quasilinear Sobolev equation and the initial-value problems of purelylongtudinal motion of a humogeneous bar, and obtained the error estimates of thistwo discrete solutions.In chapter one,we consider the mixed covolume method for the following quasi-linear Sobolev equationWe give the mixed covolumc scheme for the quasilinear Sobolev equation, and provethe mixed covolume elliptic projection has a unique solution. We also give the erroranalysis of the solution of the mixed covolume element scheme and get optimal errorestimates for the discrete scheme in L~2-norms and in H(div)-norms.In chapter two, we consider the mixed finite method for the following initial-valueproblems of purely longtudinal motion of a humogencous barWe prove the discrete formulation has a unique solution, give the mixed elliptic pro-jection, and we give the error analysis of the solution of the mixed finite element scheme and get error estimates for the discrete schemein L~2-norms.