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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Submitted on : Thursday, November 23, 2017 - 5:59:40 PM
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Alexandre Ern, Jean-Luc Guermond. Finite element quasi-interpolation and best approximation . ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, ⟨10.1051/m2an/2016066⟩. ⟨hal-01155412v3⟩

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