Some remarks on the stability coefficients and bubble stabilization of FEM on anisotropic meshes

MOX 6

Some remarks on the stability coefficients and bubble stabilization of FEM on anisotropic meshes

Monday 1st July 2002

Micheletti, Stefano; Perotto, Simona; Picasso, Marco

In this paper we re-address the anisotropic recipe provided for the stability coefficients in [13]. By comparing our approach with the residual-free bubbles theory, we improve on our a priori analysis for both the advection-diffusion and the Stokes problems. In particular, in the case of the advection-diffusion problem we derive a better interpolation error estimate by taking into account in a more anisotropic way the contribution associated with the convective term. Concerning the Stokes problem, we provide a numerical evidence that our ani -so -tro -pic approach is thoroughly comparable with the bubble stabilization, which we study more in detail in our anisotropic framework.