A Lagrange multiplier/fictitious domain method for the Dirichlet problem — Generalization to some flow problems

Abstract

In this article we discuss the solution of the Dirichlet problem for a class of elliptic operators by a Lagrange multiplier/fictitious domain method. This approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries; the resulting saddle-point system can be solved by an Uzawa/conjugate gradient algorithm. The resulting methodology is applied to the solution of some flow problems, including external incompressible viscous flow modelled by Navier-Stokes equations.