关键词: 有限元, 并行算法, 网格自适应, 误差估算, 区域分裂

Abstract: 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.

Key words: finite element, parallel computing, mesh adaptation, error estimation, domain decomposition