非线性对流扩散方程特征有限元的两重网格算法

A two-grid scheme of characteristic finite-element solution for 2D nonlinear convection-dominated diffusion problem

对非线性对流扩散方程,构造了特征有限元的两重网格算法,并给出了数值算例.此方法是先在粗网格上计算一个非线性问题,再在细网格上计算一个线性问题,数值算例表明,在计算精度保持不变的情况下,此算法可以提高非线性对流扩散问题的计算效率.

A Two-grid scheme of characteristic finite-elemen t solution for 2D nonlinear convection-dominated diffusion equation is constructed. To linearize the characteristic-method equations, it was used that a two-grid scheme to a grid ΔH much coarser than the original one Δh ,with no loss in order of accuracy so long as the mesh size obey H=O(h ). The numerical example shows the new scheme very efficiency to the nonlinear equations.