中文摘要：

给出了一种流动数值模拟中的基于误差估算的并行网格自适应有限元算法．首先，以初网格上获得的当地事后误差估算值为权，应用递归谱对剖分方法划分初网格，使各子域上总体误差近似相等，以解决负载平衡问题．然后以误差值为判据对各子域内网格进行独立的自适应处理．最后应用基于粘接元的区域分裂法在非匹配的网格上求解N-S方程．区域分裂情形下N—S方程有限元解的误差估算则是广义Stokes问题误差估算方法的推广．为验证方法的可靠性，给出了不可压流经典算例的数值结果．

英文摘要：

We present a parallel mesh adaptive finite element algorithm for numerical simulation of flows based on error estimation. The Navier-Stokes equations are solved on an initial coarse mesh to produce a posteriori error estimation. Through a recursive spectral bisection weighted by error estimation, an initial mesh is partitioned to achieve the equal error approximately in each subdomain for load balance in parallel computing. Then mesh adaptations are performed independently in each subdomain using error estimation as a criterion, Finally, by a domain decomposition method based on mortar elements, the entire problem is solved on a non-matching global mesh. The error estimation for finite element solution of Navier-Stokes equations is an extension of formulation for a generalized Stokes problem. Numerical experiments are presented to validate this algorithm.