非线性反应扩散方程的两重网格算法

将两重网格算法和混合有限元方法结合起来,通过对二维非线性反应扩散方程右端的非线性项进行基于粗网格解的泰勒展开,化为细网格上的线性问题,从而为求解该类方程提供了一种有效的数值解法。收敛性分析和数值算例结果表明,该算法与标准有限元方法相比,其优点是在不降低解的精度阶数的条件下,提高了计算速度,同时能够得到精度更高的导数。

A Two-Grid Mixed Finite-Element Method for Nonlinear Reaction Diffusion Equations

In this paper,two-grid method is combined with the mixed finite element method to carry out Taylor expansion of the right-side nonlinear item of two-dimentional and nonlinear reaction diffusion equations based on the coarse grid solution,whereby a kind of effective numerical solution is provided.The convergence analysis and numerical computing example results indicate that as compared with standard finite element method,this algorithm can improve the calculation speed with its advantages in the case of not decreasing accuracy order number of solusion and at the same time,the derivative with high accuracy can be obtained.