Abstract
In this article we generalize some standard local approximation properties of piecewise polynomials, which are measured only in the Sobolev seminorms of order 0 and 1, to the case of fractional Sobolev seminorms. The simplicity of the corresponding proofs is an interesting feature of the presentation. In addition, our analysis makes clear at each step that the constants involved are independent of the meshsizes. As an application, we show that the corresponding generalized estimates simplify the a priori error analysis of the local discontinuous Galerkin methods in the case of general non-convex polyhedral domains.
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