Zobrazeno 1 - 10
of 10
pro vyhledávání: '"Christiansen, Snorre Harald"'
Autor:
Christiansen, Snorre Harald, Hu, Kaibo
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 introduced
Externí odkaz:
http://arxiv.org/abs/1605.08657
We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schr\"odinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main new achieve
Externí odkaz:
http://arxiv.org/abs/1505.08040
Autor:
Christiansen, Snorre Harald
First we express the holonomy along a boundary curve as the integral on the domain, of an expression which is linear in the curvature. Then we provide a rigorous justification of the definition of curvature in Regge calculus.
Comment: 15 pages.
Comment: 15 pages.
Externí odkaz:
http://arxiv.org/abs/1307.3376
We show how the high order finite element spaces of differential forms due to Raviart-Thomas-N\'edelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based
Externí odkaz:
http://arxiv.org/abs/1306.4835
Autor:
Christiansen, Snorre Harald
Publikováno v:
Numerische Mathematik, Vol. 107, No. 1, p. 87-106, 2007
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological properties. The
Externí odkaz:
http://arxiv.org/abs/1007.1120
Autor:
Christiansen, Snorre Harald
Publikováno v:
Acta Numerica, Vol. 20, May 2011, p. 1-119
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance composite piec
Externí odkaz:
http://arxiv.org/abs/1006.4779
Publikováno v:
J. Math. Phys., Vol. 53, No. 3, p. 033501+17, 2012
We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting
Externí odkaz:
http://arxiv.org/abs/1006.2059
Publikováno v:
IMA J. Numer. Anal., Vol. 33, No. 1, p. 164-189, 2013
Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As an altern
Externí odkaz:
http://arxiv.org/abs/1005.2059
Publikováno v:
ENUMATH 2017-European Conference on Numerical Mathematics and Advanced Applications
ENUMATH 2017-European Conference on Numerical Mathematics and Advanced Applications, Sep 2017, Voss, Norway
ENUMATH 2017-European Conference on Numerical Mathematics and Advanced Applications, Sep 2017, Voss, Norway
International audience
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::dace573a81758eb942676048441e027c
https://hal.science/hal-01674769
https://hal.science/hal-01674769
Publikováno v:
In Comptes Rendus de l'Academie des Sciences Series I Mathematics 2000 331(9):733-738
