Abstract
Abstract : Recently the author together with R. Bank has developed, implemented and successfully applied a continuation technique for the numerical solution of parameter-dependent nonlinear elliptic boundary value problems. The method was integrated into an existing multi-grid package based on an adaptive finite element discretization. This document present the continuation method and proves an important theoretical result for the corrector iteration. For the Bratu problem - delta u = lambda e sub u on the square with homogeneous Dirichlet conditions it is shown how spurious solutions may be encountered while computing relevant solutions, how the program handles those and how it allows to detect them.
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