Abstract.We give a simple proof of existence and uniqueness of the solution of the Koiter model for linearly elastic thin shells whose midsurfaces can have charts with discontinuous second derivatives. The proof is based on new expressions for the linearized strain and change of curvature tensors. It also makes use of a new version of the rigid displacement lemma under hypotheses of regularity for the displacement and the midsurface of the shell that are weaker than those required by earlier proofs.Resume. On donne une demonstration simple de l'existence et l'unicite de la solution du modele de Koiter pour des coques minces lineairement elastiques dont les surfaces moyennes peuvent avoir des derivees secondes discontinues. La demonstration est fondee sur de nouvelles expressions des tenseurs linearises de deformation et de changement de courbure. Elle utilise egalement une version nouvelle du lemme du mouvement rigide pour une coque, sous des hypotheses de regularity du deplacement et de la surface moyenne plus faibles que celles des demonstrations anterieures.

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We present a penalized version of Naghdi's model and a mixed formulation of the same model, in Cartesian coordinates for linearly elastic shells with little regularity, and finite element approximations thereof. Numerical tests are given that validate and illustrate our approach.

We design suitable parallel in time algorithms coupled with reduction methods for the stiff differential systems integration arising in chemical kinetics. We consider linear as well as nonlinear systems. The numerical efficiency of our approach is illustrated by a realistic ozone production model.