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期刊名称: Acta Numerica
Volume:15    Page:1-155
ISSN:0962-4929

Finite element exterior calculus, homological techniques, and applications期刊论文

作者: Arnold Douglas N Falk Richard S Winther Ragnar
DOI:10.1017/S0962492906210018

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页码: 1-155
出版者: Cambridge University Press
期刊名称: Acta Numerica
ISSN: 0962-4929
语言: English
摘要: Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the PDE problem being solved. In the finite element exterior calculus, many finite element spaces are revealed as spaces of piecewise polynomial differential forms. These connect to each other in discrete subcomplexes of elliptic differential complexes, and are also related to the continuous elliptic complex through projections which commute with the complex differential. Applications are made to the finite element discretization of a variety of problems, including the Hodge Laplacian, Maxwell’s equations, the equations of elasticity, and elliptic eigenvalue problems, and also to preconditioners.
相关主题: Partial differential equations, Differential geometry, Elasticity, Homology, Calculus, Maxwell's equations, Topology, Well posed problems, Finite element method, Algebra, Mathematical analysis, Eigenvalues, Polynomials, Elliptic functions,

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