Electronic Resource
New York, NY [u.a.]
:
Wiley-Blackwell
Numerical Linear Algebra with Applications
5 (1998), S. 347-362
ISSN:
1070-5325
Keywords:
almost incompressible elasticity
;
finite elements
;
semi-coarsening refinement
;
algebraic multilevel
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio.As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd.
Additional Material:
3 Ill.
Type of Medium:
Electronic Resource
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