580 AN ADDITIVE SCHWARZ METHOD FOR THE P-VERSION FINITE ELEMENT METHOD L. Pavarino, September 1991 The additive Schwarz method was originally proposed for the h-version finite element method for elliptic problems. In this paper, we apply it to the p-version, in which increased accuracy is achieved by increasing the degree of the elements while the mesh is fixed. We obtain a constant bound, independent of p, for the condition number of the iteration operator in two and three dimensions. The result holds for linear, self adjoint, second order elliptic problems and for quadrilateral elements.