### 2009-18

by Tobiska, Lutz, Winkel, Christian.

**Series:** 2009-18, Preprints

- MSC:
- 65N12 Stability and convergence of numerical methods
- 65L10 Boundary value problems
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:**

The two-level 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. For exemple, using continuous piecewise polynomials of degree r > 1, only on function per cell is needed as enrichment instead of r in the two-level approach. Moreover, in the constant coefficient case, we derive formulas for the user-chosen stabilization parameter which guarentee that the linear of the solution becomes nodal exact.

**Keywords:**

Galerkin-Methode/Diffusionsgleichung/Diskrete Mathematik/Approximation/Finite-Elemente-Methode/Sobolev-Raum