Une méthode combinée d'éléments finis à deux grilles/bases réduites pour l'approximation des solutions d'une E.D.P. paramétrique

Abstract

In the frame of mathematical optimization procedures or parameter fitting the same problem, modeled with partial differential equations depending on a parameter has to be solved many times for different sets of parameters. The reduced basis method may be successful in this frame and recent progress have permitted to make the computations reliable thanks to a posteriori estimators and to extend the method to non linear problems thanks to the “magic points” interpolation. However, in an industrial context, it may not be possible to use the code (for example of finite element type that allows for evaluating the elements of the reduced basis) to perform all the “off-line” computations necessary for an efficient performance of the reduced basis method. We propose here an alternating approach based on a coarse grid finite element the convergence of which is accelerated through the reduced basis. To cite this article: R. Chakir, Y. Maday, C. R. Acad. Sci. Paris, Ser. I 347 (2009).