A proper feneralized decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

Agraïments: A. Nouy supported by GdR MoMaS with partners ANDRA, BRGM, CEA, CNRS, EDF, IRSNThe Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces