Uzawa type algorithm based on dual mixed variational formulation

2002 ◽  
Vol 23 (7) ◽  
pp. 765-772
Author(s):  
Wang Guang-hui ◽  
Wang Lie-heng
Keyword(s):  
Variational Formulation ◽  
Mixed Variational Formulation ◽  
Type Algorithm

A mixed variational formulation for a class of contact problems in viscoelasticity

2017 ◽  
Vol 97 (8) ◽  
pp. 1340-1356 ◽  
Author(s):  
A. Matei ◽  
S. Sitzmann ◽  
K. Willner ◽  
B. I. Wohlmuth
Keyword(s):  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Variational Formulation

Mixed Variational Formulation and Numerical Analysis of Thermally Coupled Nonlinear Darcy Flows

2013 ◽  
Vol 51 (5) ◽  
pp. 2746-2772
Author(s):  
Jiang Zhu ◽  
Jiansong Zhang ◽  
Abimael F. D. Loula ◽  
Luiz Bevilacqua
Keyword(s):  
Numerical Analysis ◽  
Variational Formulation ◽  
Mixed Variational Formulation ◽  
Darcy Flows

scholarly journals A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Yidu Yang ◽  
Wei Jiang ◽  
Yu Zhang ◽  
Wenjun Wang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Theoretical Analysis ◽  
Eigenvalue Problem ◽  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Discretization Scheme ◽  
Fine Grid ◽  
Asymptotically Optimal ◽  
Mixed Variational Formulation ◽  
Optimal Accuracy

This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems. With this scheme, the solution of an eigenvalue problem on a fine gridKhis reduced to the solution of an eigenvalue problem on a much coarser gridKHand the solution of a linear algebraic system on the fine gridKh. Theoretical analysis shows that the scheme has high efficiency. For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by takingH=O(h4), and when using thePk+1-Pkelement to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by takingH=O(h3). Finally, numerical experiments are presented to support the theoretical analysis.

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