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.
"Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows." Abstr. Appl. Anal. 2014 (SI10) 1 - 14, 2014. https://doi.org/10.1155/2014/698354