On high order finite element spaces of differential forms
نویسندگان
چکیده
منابع مشابه
On high order finite element spaces of differential forms
We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to existing choices of bases, we provide canonical resolu...
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A differential form is a field which assigns to each point of a domain an alternating multilinear form on its tangent space. The exterior derivative operation, which maps differential forms to differential forms of the next higher order, unifies the basic first order differential operators of calculus, and is a building block for a great variety of differential equations. When discretizing such...
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We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl)...
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This paper presents an efficient method for the finite element assembly of high order Whitney elements. We start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, we show how this classical approach can be reformulated into a computationally efficient matrix-matrix product. We also address the global orientation problem of the vector valued ba...
متن کاملTitle : Finite Element Differential Forms on Simplices and Cubes
s of Invited Lectures Title: Finite Element Differential Forms on Simplices and Cubes Speaker: Douglas N. Arnold Affiliation: University of Minnesota, USA Email: [email protected] Abstract: Many applications require finite element discretizations of the spaces of differential forms comprising the de Rham complex. In three dimensions, this means constructing finite element subspaces of H, H(curl), ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2015
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/2995