کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
499066 863026 2009 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Geometric decompositions and local bases for spaces of finite element differential forms
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Geometric decompositions and local bases for spaces of finite element differential forms
چکیده انگلیسی

We study the two primary families of spaces of finite element differential forms with respect to a simplicial mesh in any number of space dimensions. These spaces are generalizations of the classical finite element spaces for vector fields, frequently referred to as Raviart–Thomas, Brezzi–Douglas–Marini, and Nédélec spaces. In the present paper, we derive geometric decompositions of these spaces which lead directly to explicit local bases for them, generalizing the Bernstein basis for ordinary Lagrange finite elements. The approach applies to both families of finite element spaces, for arbitrary polynomial degree, arbitrary order of the differential forms, and an arbitrary simplicial triangulation in any number of space dimensions. A prominent role in the construction is played by the notion of a consistent family of extension operators, which expresses in an abstract framework a sufficient condition for deriving a geometric decomposition of a finite element space leading to a local basis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 198, Issues 21–26, 1 May 2009, Pages 1660–1672
نویسندگان
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