The Whitney elements, discrete spaces based on differential forms, have proven their efficiency in electromagnetic field computation. However, they are built only in first order. This paper gives a general description of high order p-form (nodal, edge, facet and volume) elements. Their function spaces and the assignment of degrees of freedom on the simplexes are analyzed. General expressions of the basis functions are given. A comparison of several 2nd order elements is carried out. A procedure for the generation of the hierarchical basis of p-form elements is provided.
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Ida et al. (2000) studied this question.
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