A novel parallel two-step algorithm based on finite element discretization for the incompressible flow problem

Abstract

Based on a two-step finite element method and fully overlapping domain decomposition technique, a parallel two-step algorithm for the incompressible flow problem is introduced and analyzed. In the new algorithm, all of the computations are performed in parallel on global composite meshes which are fine around the subdomain that we concentrate on but coarse elsewhere. Each processor first solves an original problem based on the P₁–P₁ stabilized finite element method and then solves a generalized Stokes problem based on the P₂–P₂ stabilized finite element method on a global composite mesh. The proposed algorithm is easy to implement. What’s more, the new algorithm can yield more accurate solutions compared with the numerical solution obtained by the common two-step method. Numerical tests are presented to verify the efficiency and validity of the proposed algorithm.

Additional information

Funding

This work is in part supported by the NSF of China [Nos. 11671345, 11362021 and 41501107], the Research Fund from Key Laboratory of Xinjiang Province [No. 2017D04030], and the NSF of Xinjiang Province [Nos. 2016D01C058 and 2015211C289].