Finite element quasi-interpolation and best approximation
نویسندگان
چکیده
This paper introduces a quasi-interpolation operator for scalarand vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces W r,p, where p ∈ [1,∞] and the smoothness index r can be arbitrarily close to zero. The operator is stable in L, leaves the corresponding finite element space point-wise invariant, and can be modified to handle homogeneous boundary conditions. The theory is illustrated on H-, H(curl)and H(div)-conforming spaces.
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