SCAIM Seminar: Brian Wetton (UBC)

Implicit time stepping applied to discretized incompressible fluid flow problems results in discrete Stokes-like (saddle-point, KKT) problems. There is a class of so-called Projection Methods in which these Stokes-like problems are efficiently approximated by the solutions of standard, second order elliptic problems. Over the last 20 years, these methods have been increasingly well understood. In this talk, a review of the methods and the analytic results are given. Leading order errors (both character and order) from the methods can be precisely described using asymptotic techniques. This asymptotic error analysis is applied to a number of commonly used projection methods. The results are confirmed by careful numerical computations using a spectral method on a representative model problem.