Pressure stability in fractional step finite element methods for incompressible flows

Abstract

The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows. For the classical first order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second order scheme in which part of the extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.