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On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces


Author: Snorre H. Christiansen
Journal: Math. Comp. 87 (2018), 547-580
MSC (2010): Primary 65N30, 65N25, 81Q05
DOI: https://doi.org/10.1090/mcom/3233
Published electronically: August 7, 2017
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Abstract: We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms, such as those arising from electromagnetic fields, we develop some abstract discretization theory and provide estimates in fractional order Sobolev spaces for finite element systems. Eigenmode convergence is proved, as well as optimal convergence orders, assuming a flat background metric on a periodic domain.


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Additional Information

Snorre H. Christiansen
Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway
Email: snorrec@math.uio.no

DOI: https://doi.org/10.1090/mcom/3233
Keywords: Dirac equation, finite elements, differential forms, fractional Sobolev spaces, mollified interpolator.
Received by editor(s): December 7, 2015
Received by editor(s) in revised form: September 16, 2016, October 13, 2016, and October 29, 2016
Published electronically: August 7, 2017
Additional Notes: This research was supported by the European Research Council through the FP7-IDEAS-ERC Starting Grant scheme, project 278011 STUCCOFIELDS
Article copyright: © Copyright 2017 American Mathematical Society

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