Reply [to “Comment on ‘Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?’ by R. Mosé, P. Siegel, P. Ackerer, and G. Chavent”]

1996 ◽  
Vol 32 (6) ◽  
pp. 1911-1913 ◽  
Author(s):  
P. Ackerer ◽  
R. Mosé ◽  
P. Siegel ◽  
G. Chavent
Keyword(s):  
Finite Element ◽  
Groundwater Flow ◽  
Flow Model ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Groundwater Flow Model ◽  
Hybrid Finite Element ◽  
Mixed Hybrid Finite Element

Iterative Solutions of a Mixed Hybrid Finite Element Scheme for the Signorini Problem

2004 ◽  
Vol 4 (2) ◽  
pp. 180-191
Author(s):  
Marina A. Ignatieva ◽  
Alexander V. Lapin
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Signorini Problem ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Mixed Hybrid Finite Element ◽  
The Laplace Operator

AbstractA mixed hybrid finite element method of the lowest order is studied for the Signorini problem. An iterative method with a preconditioner being a classical finite element approximation of the Laplace operator is constructed. A multistage iterative procedure for the mixed hybrid finite element scheme is constructed, the rate of convergence and the complexity of this method are analysed.

Mixed Hybrid Finite Element Method for a Variational Inequality with a Quasi-linear Operator

2009 ◽  
Vol 9 (4) ◽  
pp. 354-367 ◽  
Author(s):  
A. Lapin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Inequality ◽  
Domain Decomposition Method ◽  
Linear Differential Operator ◽  
Element Approximation ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Mixed Hybrid Finite Element ◽  
Element Method

Abstract A mixed hybrid finite element method has been applied to a variational inequality with a potential second-order quasi-linear differential operator. The Lagrange multiplier method for a dual problem has been used to construct this finite element scheme. The existence and uniqueness of a solution for the resulting finite- dimensional problem has been proved, the solution iterative methods are discussed. The non-overlapping domain decomposition method combined with the mixed hybrid finite element approximation is analyzed.

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