Decomposition of energy spaces and applications

In this Note we discuss the solution of linear variational problems in Hilb ert spaces V, such that V = Sigma(i=1)(m) V-i, with the possibility that V- i n boolean AND V-j not equal {0} if i not equal j. We take advantage of th e above decomposition of V to solve the linear variational problems by conj ugate gradient algorithms operating in IIi=1m V-i. For some situations, the method discussed in this note leads to novel domain decomposition methods with good convergence and parallelization properties. We conclude this note with the results of numerical experiments concerning the solution of ellip tic problems on an L-shaped domain considered as the union of two overlappi ng rectangles and on a two-dimensional domain which is the union of a recta ngle and a disk. (C) 1999 Academie des Sciences/Editions scientifiques et m edicales Elsevier SAS.