一类二维非线性发展方程的交替方向有限体积元方法

Alternating Direction Finite Volume Element Method for a Class of Two Dimensional Nonlinear Evolution Equation

采用交替方向有限元方法的离散思想,利用差分方法中的Douglas格式,给出了求解一类二维非线性发展方程的基于双线性插值的交替方向有限体积元法.文中对该方法进行了误差估计,并用数值例子验证了方法的有效性.

By using the discretizing idea about alternating-direction FEM and applying Douglas scheme in FDM, this paper gives the alternating direction finite volume element method for a class of nonlinear evolution equation based on linear interpolation. This paper also gives the error estimates. Finally, a numerical example shows that the method is very effective for solving this problem.