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FINITE ELEMENT QUASI-INTERPOLATION AND BEST APPROXIMATION

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01155412
Contributor : Alexandre Ern <>
Submitted on : Tuesday, May 26, 2015 - 3:52:11 PM
Last modification on : Saturday, May 30, 2015 - 1:06:34 AM
Long-term archiving on: : Monday, April 24, 2017 - 3:06:52 PM

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  • HAL Id : hal-01155412, version 1

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Alexandre Ern, Jean-Luc Guermond. FINITE ELEMENT QUASI-INTERPOLATION AND BEST APPROXIMATION . 2015. ⟨hal-01155412v1⟩

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