We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.

Mixed finite elements in ℝ 3

The use of finite elements to discretize the time dependent Maxwell equations on a bounded domain in three-dimensional space is analyzed Energy norm error estimates are provided when general finite element methods are used to discretize the equations in space In addition, it is shown that if some curl conforming elements due to Nedelec are used, error estimates may also be proved in the $L^2 $ norm

Analysis of a finite element method for Maxwell's equations

https://cnls.lanl.gov/~shashkov/papers/maxjcp.pdf

Mimetic Discretizations for Maxwell's Equations

A semidiscrete mixed finite element approximation to the time dependent Maxwell's equations on a bounded smooth domain is analyzed. A variational problem for the electric and magnetic fields in which the boundary conditions are enforced naturally is derived. Then a general convergence result for mixed methods is proven, and it is shown how this result may be used to prove various error estimates when Nedelec's curl conforming finite elements are used. JZ3 with connected boundary F and unit outward normal n. Let e(x) and /1(x) denote, respectively, the dielectric constant and magnetic permeability of the medium occupying Q. Let a(x) denote the conductivity of the medium. Then, if E(x, t) and H(x, t) denote, respectively, the electric and magnetic fields, Maxwell's equations (10) state that

A mixed method for approximating Maxwell's equations

https://www.ki-net.umd.edu/pubs/files/FRG-2009-Degond-Pierre.PICAP_03_feb_09.pdf

P.A. Raviart

Papers

Study of an implicit scheme for integrating Maxwell's equations