The Characteristic Finite Element Method For Nonlinear Equations With Convection-dominated Diffusion

The paper mainly includes two parts as following:In the first part,we discuss the characteristic-mixed finite element methods for miscible displacement in porous media.First we use the nonconforming CNQ₁^rot element to approximate the concentration of the first component,CNQ₁^rot×CNQ₁^rot and Q0 to approximate the velocity and the pressure of the fluid mixture respectively to build the approximation scheme of the characteristic finite element,then by use of the special characters of CNQ₁^rot element and combining with the average skill,the superclose results of relevant variables are derived for this scheme.In the second part,we study the characteristic-mixed finite element nethod about the nonconforming EQ₁?rot? for nonlinear Sobolev equation.By use of two important prop-erties of EQ₁?rot?,the superclose estimate of the original variable is derived for this scheme.