[Back]

M. Karkulik, J. Melenk:
"Local high-order regularization and applications to hp-methods (extended version)";
in: "ASC Report 38/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 38.

We develop a regularization operator based on smoothing on a locally defined length scale. This operator is defined on L1 and has approximation properties that are given by the local
regularity of the function it is applied to and the local length scale. Additionally, the regularized function satisfies inverse estimates commensurate with the approximation orders. By combining
this operator with a classical hp-interpolation operator, we obtain an hp-Cl´ement type quasiinterpolation operator, i.e., an operator that requires minimal smoothness of the function to be
approximated but has the expected approximation properties in terms of the local mesh size and polynomial degree. As a second application, we consider residual error estimates in hp-boundary
element methods that are explicit in the local mesh size and the local approximation order.

Cl´ement interpolant, quasi-interpolation, hp-FEM, hp-BEM

http://www.asc.tuwien.ac.at/preprint/2014/asc38x2014.pdf