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.

NUMERICAL METHODS OF NEW MIXED FINITE ELEMENT SCHEME FOR SINGLE-PHASE COMPRESSIBLE FLOW

2013 ◽  
Vol 11 (01) ◽  
pp. 1350055 ◽  
Author(s):  
SHUYING ZHAI ◽  
XINLONG FENG ◽  
ZHIFENG WENG
Keyword(s):  
Finite Element ◽  
Compressible Flow ◽  
Single Phase ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Conforming Finite Element

In this paper, a new mixed finite element scheme is given based on the less regularity of velocity for the single phase compressible flow in practice. Based on the new mixed variational formulation, we give its stable conforming finite element approximation for the P0–P1 pair and its stabilized conforming finite element approximation for the P1–P1 pair. Moreover, optimal error estimates are derived in H1-norm and L2-norm for the approximation of pressure and error estimate in L2-norm for the approximation of velocity by using two methods. Finally, numerical tests confirm the theoretical results of our methods.

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