High-Order Optimal Edge Elements for Pyramids, Prisms and Hexahedra

Morgane Bergot (1) , Marc Duruflé (2, 3)

1 CALVI - Scientific computation and visualization
2 IMB - Institut de Mathématiques de Bordeaux
3 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems

Edge elements are a popular method to solve Maxwell's equations especially in time-harmonic domain. However, when non-affine elements are considered, elements of the Nedelec's first family are not providing an optimal rate of the convergence of the numerical solution toward the solution of the exact problem in H(curl)-norm. We propose new finite element spaces for pyramids, prisms, and hexahedra in order to recover the optimal convergence. In the particular case of pyramids, a comparison with other existing elements found in the literature is performed. Numerical results show the good behaviour of these new finite elements.

Mots clés: Edge elements; High-order finite element; Pyramids; Maxwell's equations

Domaines: Equations aux dérivées partielles [math.AP]

Morgane Bergot, Marc Duruflé. High-Order Optimal Edge Elements for Pyramids, Prisms and Hexahedra. Journal of Computational Physics, 2013, 232 (1), pp.189-213. ⟨10.1016/j.jcp.2012.08.005⟩. ⟨hal-00605963v2⟩