A mathematical formulation suitable for the application of a novel Hermite finite element method, to solve electromagnetic field problems in two- and three-dimensional domains is studied. This approach offers the possibility to generate accurate approximations of Maxwell’s equations in smooth domains, with a rather rough interpolation and without curved elements. Method’s degrees of freedom are the normal derivative mean values of the electric field across the edges or the faces of a mesh consisting of N-simplices, in addition to the mean value in the mesh elements of the field itself. Second-order convergence of the electric field in the mean-square sense and first-order convergence of the magnetic field in the same sense are rigorously established, if the domain is a convex polytope. Numerical results for two-dimensional problems suggest however that second-order convergence can also be expected of the magnetic field. Both behaviors are shown to apply to the case of curved domains as well, provided a simple interpolated boundary condition technique is employed.
Digital Object Identifier (DOI)
Ruas, Vitoriano and Antonio Silva Ramos, Marco
"A Hermite Method for Maxwell’s Equations,"
Applied Mathematics & Information Sciences: Vol. 12
, Article 1.
Available at: https://dc.naturalspublishing.com/amis/vol12/iss2/1