The two-level local projection stabilization as an enriched one-level approach

Abstract

The two-level local projection stabilization is considered as a one-level approach in which the enrichments on each element are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the convergence order. On triangular meshes, for example, using continuous piecewise polynomials of degree r???1, only 2r???1 functions per macro-cell are needed for the enrichment compared to r 2 in the two-level approach. In case of the Stokes problem r???1 functions per macro-cell are already sufficient to guarantee stability and to preserve convergence order. On quadrilateral meshes the corresponding reduction rates are even higher. We give examples of "reduced" two-level approaches and study how the constant in the local inf-sup condition for the one-level and different two-level approaches, respectively, depends on the polynomial degree r.