Abstract

In this article, we mainly propose and analyze a parallel stabilized finite element algorithm based upon two-grid discretization for the Navier-Stokes problem. The lowest equal-order finite element pairs are considered for the finite element discretization and a stabilized term based on two local Gauss integrations is introduced to circumvent the discrete inf-sup condition. The main idea is to utilize a partition of unity to assemble weighted local corrections of solutions on sub-domains. A further coarse grid correction is carried out to derive the optimal error estimates both in H1 norm and L2 norm. Theoretical results are rigorously established and some numerical experiments are reported to verify the theoretical results.

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