Generalized finite element systems for smooth differential forms and Stokes’ problem

Generalized finite element systems for smooth differential forms and Stokes’ problem Numerische Numer. Math. https://doi.org/10.1007/s00211-018-0970-6 Mathematik Generalized finite element systems for smooth differential forms and Stokes’ problem 1 1 Snorre H. Christiansen · Kaibo Hu Received: 26 August 2016 / Revised: 22 January 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously intro- duced notion of finite element systems, and the examples include conforming mixed finite elements for Stokes’ equation. In dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes. In dimension 3 we define one low order complex, which may be branched into Whitney forms at a chosen index. Stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension. The finite element spaces all consist of composite polynomials. The framework guarantees some nice properties of the spaces, in partic- ular the existence of commuting interpolators. It also shows that some of the examples are minimal spaces. Mathematics Subject Classification 65N30 · 58A12 1 Introduction This article is http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

Generalized finite element systems for smooth differential forms and Stokes’ problem

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0029-599X
eISSN
0945-3245
D.O.I.
10.1007/s00211-018-0970-6
Publisher site
See Article on Publisher Site

Abstract

Numerische Numer. Math. https://doi.org/10.1007/s00211-018-0970-6 Mathematik Generalized finite element systems for smooth differential forms and Stokes’ problem 1 1 Snorre H. Christiansen · Kaibo Hu Received: 26 August 2016 / Revised: 22 January 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously intro- duced notion of finite element systems, and the examples include conforming mixed finite elements for Stokes’ equation. In dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes. In dimension 3 we define one low order complex, which may be branched into Whitney forms at a chosen index. Stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension. The finite element spaces all consist of composite polynomials. The framework guarantees some nice properties of the spaces, in partic- ular the existence of commuting interpolators. It also shows that some of the examples are minimal spaces. Mathematics Subject Classification 65N30 · 58A12 1 Introduction This article is

Journal

Numerische MathematikSpringer Journals

Published: May 28, 2018

References

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