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Interpolation, Projection and Hierarchical Bases in Discontinuous Galerkin Methods

Part of: Numerical approximation and computational geometry Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  05 August 2015

Lutz Angermann  and
Christian Henke
Lutz Angermann*
Affiliation:
Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678 Clausthal-Zellerfeld, Germany
Christian Henke
Affiliation:
Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678 Clausthal-Zellerfeld, Germany
*
*Email addresses: lutz.angermann@tu-clausthal.de (L. Angermann), henke@math.tu-clausthal.de (C. Henke)
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Abstract

The paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based on hierarchical bases, and on inverse inequalities.

Keywords

Interpolationquadraturehierarchical basesinverse inequalities

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65D32: Quadrature and cubature formulas
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015 , pp. 425 - 450
Copyright
Copyright © Global-Science Press 2015 

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