High Accuracy Analysis Of A New Mixed Finite Element Scheme For Nonlinear Parabolic Equations

This dissertation is mainly studied the superconvergence property and fully discrete analysis for the nonlinear parabolic equation in new mixed finite element schemes. At first, new mixed finite element schemes are constructed for nonlinear parabolic equations by utilizing the conforming element of order p and the nonconforming EQ1rot element. By means of the average value、the integral identities and interpolation post processing techniques, the superclose and superconvergence results of original variables and flux are obtained for a semi-discrete scheme. Because of the reasonable choice of the space, the BB condition in the format is obviously satisfied. Then, making use of the bilinear element of the smallest freedom, we construct a new backward Euler and Crank-Nicolson fully discrete mixed finite element scheme. The error estimates of original variables u and flux p in L2-model significance is derived by using the above techniques.