Differential forms, fluids, and finite models
نویسندگان
چکیده
منابع مشابه
Differential Forms, Fluids, and Finite Models
By rewriting the Navier-Stokes equation in terms of differential forms we give a formulation which is abstracted and reproduced in a finite dimensional setting. We give two examples of these finite models and, in the latter case, prove some approximation results. Some useful properties of these finite models are derived.
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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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We discuss the tensor product construction for complexes of differential forms and show how it can be applied to define shape functions and degrees of freedom for finite element differential forms on cubes in n dimensions. These may be extended to curvilinear cubic elements, obtained as images of a reference cube under diffeomorphisms, by using the pullback transformation for differential forms...
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: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11003-7