Whitney Forms of Higher Degree

Abstract : Low-order Whitney elements are widely used for electromagnetic field problems. Higher-order approximations are receiving increasing interest, but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to p-chains. We provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom. Properties of the higher-order Whitney complex are deeply investigated.
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Submitted on : Tuesday, December 11, 2012 - 4:58:39 PM
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Francesca Rapetti, Alain Bossavit. Whitney Forms of Higher Degree. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (3), pp.2369-2386. ⟨10.1137/070705489⟩. ⟨hal-00763881⟩

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