Two-Grid Finite Element Discretization Schemes Based on Shifted-Inverse Power Method for Elliptic Eigenvalue Problems

2011 ◽  
Vol 49 (4) ◽  
pp. 1602-1624 ◽  
Author(s):  
Yidu Yang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Eigenvalue Problems ◽  
Inverse Power ◽  
Power Method ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Discretization Schemes ◽  
Elliptic Eigenvalue Problems

scholarly journals Finite element exterior calculus, homological techniques, and applications

Acta Numerica ◽  
2006 ◽  
Vol 15 ◽  
pp. 1-155 ◽  
Author(s):  
Douglas N. Arnold ◽  
Richard S. Falk ◽  
Ragnar Winther
Keyword(s):  
Finite Element ◽  
Algebraic Topology ◽  
Eigenvalue Problems ◽  
Differential Forms ◽  
Element Discretization ◽  
Hodge Laplacian ◽  
Finite Element Exterior Calculus ◽  
Exterior Calculus ◽  
Elliptic Eigenvalue Problems ◽  
Elliptic Complex

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.

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