【Workshop postponed, future dates TBD】Workshop on Computational Fluid Dynamics and Uncertainty Quantification

## An Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations

### Speaker

Yanren Hou , Xi’an Jiaotong University

### Abstract

 In this talk, an expandable local and parallel two-grid finite element scheme based on superposition principle for the Stokes equations is proposed and analyzed. Compared with the usual local and parallel finite element schemes, the scheme considered here can be easily implemented in a large parallel computer system, which has a lot of computing cores. Convergence results base on $H^1$ and $L^2$ a priori error estimations of the scheme are obtained, which show that the scheme can produce approximate solution with optimal convergence orders within $\ln H ^2$ or $\ln H$ times two-grid iterations if the coarse mesh size $H$ and the fine mesh size $h$ are properly configured in 2-D or 3-D case, respectively. Some numerical results are presented to support the analysis results.