On eigenmode approximation for Dirac equations: differential forms and fractional Sobolev spaces
Numerical Analysis
2016-09-19 v3
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 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.
Cite
@article{arxiv.1511.06272,
title = {On eigenmode approximation for Dirac equations: differential forms and fractional Sobolev spaces},
author = {Snorre H. Christiansen},
journal= {arXiv preprint arXiv:1511.06272},
year = {2016}
}
Comments
24 pages. v2: numerous typos corrected, all results now proved. v3: 36 pages, convergence orders now included