非线性反应扩散问题两网格混合有限元法的数值分析

Numerical Analysis of a Two-Grid Mixed Finite Element Method for Nonlinear Reaction-Diffusion Problems

对于一类非线性反应扩散问题,给出了一种两网格混合有限元解法.首先在粗网格上求解非线性方程组,然后在细网格上采用了牛顿迭代求解.从数值分析的角度对两网格混合有限元算法进行了研究.数值算例结果表明,与混合有限元方法相比,两网格混合有限元方法在不降低解的精度阶数的条件下,提高了计算速度.

For a kind of nonlinear reaction-diffusion problems, a two-grid mixed finite element method is investigated. First, the original nonlinear equations are solved on the coarse grid. Then, Newton iteration on the fine grid is used and numerical analysis is carried out. Numerical experimental results indicate that the two-grid mixed finite element method has improved the calculation speed in the case of not decreasing the accuracy order number of the solution.