A Class Of Nonlinear Evolution Equations, Finite Volume Element Method

This paper considers the finite volume element method (FVEM) for a class of nonlinear evolution equation. The main work of the dissertation can be summarized as follows:1. Chapter 1 gives a full discrete finite volume element method for a class of one dimensional nonlinear evolution equation which bases on a piecewise linear element space. The error estimates in L~2 and H~1 norms are obtained. At last, a numerical experiment demonstrates that the method is very effective.2. Chapter 2 develops the alternating direction finite volume element method for a class of two dimensional nonlinear evolution equation (i.e. the nonlinear heat transport equation) by using the discretizing idea about alternating-direction FEM, and further gives two kinds of computational schemes. It also analyzes the schemes which have second order convergence accuracy with respect to discrete L~2 norm. Finally, results of numerical tests are given.