一种新的并行自适应网格有限元算法

给出了一种新的适用于流体力学问题的并行自适应有限元算法。首先，基于初始稀网格上获得的事后误差估算值，应用反复谱对剖分方法对初网格进行划分，使各子域上总体误差近似相等，从而解决并行自适应计算中的负载平衡问题。然后在各处理器上独立地求解整体问题，并进行指定子域上的网格自适应处理。最后将各子域上的自适应网格组合成一个整体网格，应用基于粘接元技术的区域分裂法在该网格上获得最终解。文末给出了数值实验结果。

A new parallel adaptive finite element algorithm

A new parallel adaptive finite element algorithm for the partial differential equation(s) in fluid mechanics has been presented. At first, the equation(s) is solved on an initial coarse mesh to produce a posteriori\|error estimate. Through a recursive spectral bisection based on the error estimate, the initial mesh is partitioned to achieve approximately equal error in each subregion for the load balance in parallel computing. Then, the entire problem is solved independently on each processor and the mesh adaptation is confined largely in its own partition. Finally, the adapted meshes taken from each subregion form a non matching global mesh and the entire problem is solved on it to obtain the final solution, using a domain decomposition method based on mortar elements. At the end of the paper, the results of numerical experiments are given to verify this algorithm.