Finite element method based on combination of "saddle point" variational formulations

A modified mixed/hybrid finite element method, which is no longer required to satisfy the Babuska-Brezzi condition, is referred to as a stabilized method Based on the duality of vanational principles in solid mechanics, a new type of stabilized method, called the combinatorially stabilized mixed/hyb...

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Bibliographic Details
Published in:Science China. Technological sciences 1997-06, Vol.40 (3), p.285-300
Main Author: 周天孝
Format: Article
Language:English
Subjects:
element
error
estimates
finite
Finite element method
method
mixed/hybrid
point
problem
saddle
Saddle points
Solid mechanics
Stability analysis
stabilized
Variational principles
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Summary:A modified mixed/hybrid finite element method, which is no longer required to satisfy the Babuska-Brezzi condition, is referred to as a stabilized method Based on the duality of vanational principles in solid mechanics, a new type of stabilized method, called the combinatorially stabilized mixed/hybrid finite element method, is presented by weight-averaging both the primal and the dual "saddle-point" schemes. Through a general analysis of stability and convergence under an abstract framework, it is shown that for the methods only an inf-sup inequality much weaker than Babuska-Brezzi condition needs to be satisfied. As a concrete application, it is concluded that the combinatorially stabilized Raviart and Thomas mixed methods permit the C -elements to replace the H(div; Ω)-elements.
ISSN:1674-7321
1006-9321
1869-1900
1862-281X
DOI:10.1007/BF02916604