TY - JOUR T1 - A New Parallel Finite Element Algorithm Based on Two-Grid Discretization for the Generalized Stokes Problem JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 676 EP - 688 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/459.html KW - Generalized Stokes problem, finite element, parallel algorithm, Schwarz method, two-grid method. AB -

Based on two-grid discretization, a new parallel finite element algorithm for the generalized Stokes problem is proposed and analyzed. Motivated by the observation that for a solution to the generalized Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid, this algorithm first solves the generalized Stokes problem on a coarse grid, and then corrects the resulted residual by standard additive Schwarz method on a fine grid. Under some regular assumptions, error estimates of the approximate solutions are provided. Numerical results are also given to illustrate the effectiveness of the algorithm.