Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows

Abstract EN

We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method.

The stability and error estimates of finite element solutions are derived for classical one-level method.

Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods.

We also propose a new Newton correction scheme based on the above two-level iteration methods.

Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.