Some refined finite volume element methods for the Stokes and Navier–Stokes systems with corner singularities

Abstract

It is well known that the solution of the Stokes or Navier–Stokes system in a non convex polygonal domain of has a singular behaviour near non convex corners. Consequently we investigate different refined (non conforming) finite volume-element methods to approximate the solution of such problems and restore optimal orders of convergence as for smooth solutions. Numerical tests are presented, which confirm the theoretical rates of convergence and illustrate the advantage of the use of refined meshes.