Stabilized mixed finite element methods based on Riesz-representing operators for solving saddle point problems

Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not subject to the discrete Babus̆ka–Brezzi condition, and that the corresponding finite element approximation problem yields a symmetrically positiv...

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Published inComputer methods in applied mechanics and engineering Vol. 188; no. 1; pp. 257 - 268
Main Author Duan, Huo-yuan
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.07.2000
Elsevier
Subjects
Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Local bubble functions
Mathematical methods in physics
Physics
Riesz-representing operator
Saddle point problem
Stabilized mixed finite element method
The Stokes equation
The Stokes equation
Saddle point problem
Riesz-representing operator
Local bubble functions
65N30
Stabilized mixed finite element method
Finite element method
Linear systems
Stokes problem
Stokes equation
Saddle-point method
Numerical method
Mixed method
Riesz operator
Saddle point
Online AccessGet full text
ISSN0045-7825
1879-2138
DOI10.1016/S0045-7825(99)00151-6

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Abstract Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not subject to the discrete Babus̆ka–Brezzi condition, and that the corresponding finite element approximation problem yields a symmetrically positively definite linear system. Error bounds are obtained which are agree with the interpolation properties. As an application, the stationary Stokes problem is analyzed.
AbstractList Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not subject to the discrete Babuska-Brezzi condition, and that the corresponding finite element approximation problem yields a symmetrically positively definite linear system. Error bounds are obtained which are agree with the interpolation properties. As an application, the stationary Stokes problem is analyzed.
Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not subject to the discrete Babus̆ka–Brezzi condition, and that the corresponding finite element approximation problem yields a symmetrically positively definite linear system. Error bounds are obtained which are agree with the interpolation properties. As an application, the stationary Stokes problem is analyzed.
Author huo-yuan, Duan
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Cites_doi 10.1016/0045-7825(88)90168-5
10.1137/0728084
10.1007/BF02165003
10.1137/0731091
10.1017/CBO9780511574856.005
10.1007/BF01395886
10.1007/s11766-999-0044-8
10.1137/0731071
10.1002/num.1690050307
10.1090/S0025-5718-1985-0771031-7
10.1016/0045-7825(95)00826-M
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Issue 1
Keywords The Stokes equation
Saddle point problem
Riesz-representing operator
Local bubble functions
65N30
Stabilized mixed finite element method
Finite element method
Linear systems
Stokes problem
Stokes equation
Saddle-point method
Numerical method
Mixed method
Riesz operator
Saddle point
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Snippet Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not...
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SubjectTerms Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Local bubble functions
Mathematical methods in physics
Physics
Riesz-representing operator
Saddle point problem
Stabilized mixed finite element method
The Stokes equation
Title Stabilized mixed finite element methods based on Riesz-representing operators for solving saddle point problems
URI https://dx.doi.org/10.1016/S0045-7825(99)00151-6
https://www.proquest.com/docview/27711042
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