ABSTRACT
DENISE CHENAIS and MARTIN ZERNER Laboratoire de mathematiques , CNRS , Universite de Nice, BP71 , F-06108 Nice Cedex, France
JEAN-CLAUDE PAUMIER L .M .C . , CNRS , IMAG, BP53, Cedex 9, F-38041 Greno ble, France
Abstract . We study the numerical approximation of the solution of elliptic linear equations depending on a real parameter t E [0 , 1 ] ' in infinite dimensional vector spaces . The solution is assumed to exist and to be unique for any given t E ]O , 1 ] , but for t = 0 , the kernel of the operator is not reduced to {O } . The paper is separated into two parts : necessary conditions on the one hand, sufficient conditions on the other hand. In both parts we study first the abstract setting, then we apply it to the computation of the linear behavior of an arch governed by a Kirchhoff-Love model . The small parameter is the thickness of the arch.
