Multigrid for finite-element discretizations of the equations of aerodynamics

A multigrid algorithm for the solution of finite element stabilized discretization of compressible fluid dynamics equations on unstructured grids is described. Solution of the stationary problems is seached by time-stepping and a linearization of the non-linear discrete systems leads to a very large system of linear equations. These systems are ill-conditioned and require efficient computational procedures. The numerical experiments for Navier–Stokes and Euler systems are presented. The method can be easily included in a parallel library as preconditioner.