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

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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 arizing from electromagnetic fields, we develop some abstract discretization theory and provide estimates in fractional Sobolev spaces for finite element systems. Eigenmode convergence is proved, assuming a flat background metric on a periodic domain.

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          Author and article information

          Journal
          2015-11-19
          2015-12-03
          Article
          1511.06272
          7d3d893a-1318-4012-9d1c-2035241ccfbd

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          65N30, 65N25, 81Q05
          24 pages. v2: numerous typos corrected, all results now proved
          math.NA

          Numerical & Computational mathematics
          Numerical & Computational mathematics

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