On eigenmode approximation for Dirac equations: differential forms and fractional Sobolev spaces
Provides theoretical foundations for finite element discretization of Dirac equations, relevant for computational physics and numerical analysis.
The paper develops abstract discretization theory for Dirac equations using finite element spaces of differential forms, proving eigenmode convergence and optimal convergence orders for periodic domains with flat metric.
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.