Reduced finite element discretizations of the Stokes and Navier-Stokes equations

Abstract

We consider velocity spaces being a direct sum two finite element spaces, one of which is needed only to fulfil the Babuška-Brezzi condition. The splitting of the velocity space gives rise to a number of terms in the discrete problem.

We show that not all these terms are necessary for the solvability of the discrete problem and for optimal convergence properties of the discrete solutions.

Keywords

• Reduced
• finite
• element
• discretizations
• Stokes
• Navier-Stokes
• equations