一维对流扩散问题的移动有限点方法

The Moving Finite Point Method for One Dimensional Convection-Diffusion Problems

研究一种新的无网格方法:移动有限点方法,其思想是将有限点方法和移动网格技巧相结合,利用等弧长原理移动网格自适应地产生节点分布,在此基础上运用有限点方法求解对流扩散问题.给出了理论基础和算法流程,数值实验验证了移动有限点方法可以得到更精确的结果,并有最优的2阶收敛率.

We propose a new meshless method, i. e. , the moving finite point method, whose idea is combining the finite point method with the moving mesh technique to distribute the points adaptively by the equal arc-length principle in an iterative way. Then the finite point method is applied to solve the one-dimensional convection-diffusion problem. We first outline the theoretical background and program. Then the numerical experiments confirm that this approach can acquire more accurate results and optimal second order convergence rate compared with the up-winding moving mesh method.