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A high order mixed vector finite element method for solving the time dependent Maxwell equations on unstructured grids. (English) Zbl 1073.78010

The paper presents a mixed vector finite element method for discretizing the time dependent Maxwell equations on unstructured hexahedral grids that is of arbitrary order accuracy in space and up to 4th order accurate in time. The method is charge and energy conserving, conditionally stable and correctly models both the jump discontinuities and the divergence-free properties of the electric and magnetic fields. Several computational examples are performed to demonstrate the benefits of the method, including the improved reduction of numerical dispersion error for electrically large problems.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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