On the convergence of block constrained nonlinear equation solvers∗

The shortcomings associated with successive substitution nonlinear solvers are circumvented by introducing a so-called block constraint methodology. Specifically, by partitioning the governing field equations into various subsets, constraints can be applied individually to each separate block. To illustrate the formal properties of the scheme, a series of lemmas and a theorem will be developed. These define its convergence properties. Due to the generality of the approach taken, virtually any form of functional constraint may be employed.