FINITE ELEMENT QUASI-INTERPOLATION AND BEST APPROXIMATION

Alexandre Ern (1, 2) , Jean-Luc Guermond (3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
3 TAMU - Department of Mathematics [Texas]

This paper introduces a quasi-interpolation operator for scalar-and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator is stable in L^1 , is a projection, whether homogeneous boundary conditions are imposed or not, and, assuming regularity in the fractional Sobolev spaces W^{s,p} where p ∈ [1, ∞] and s can be arbitrarily close to zero, gives optimal local approximation estimates in any L^p-norm. The theory is illustrated on H^1-, H(curl)-and H(div)-conforming spaces.

Mots clés: Quasi-interpolation; Finite Elements; Best Approximation; AMS subject classifications 65D05; 65N30; 41A65

Domaines: Analyse numérique [math.NA]

Alexandre Ern, Jean-Luc Guermond. FINITE ELEMENT QUASI-INTERPOLATION AND BEST APPROXIMATION . 2015. ⟨hal-01155412v2⟩