ON CONTINUATION FOR VARIATIONAL INEQUALITIES.

While many continuation methods for the numerical solution of nonlinear eigenvalue problems for ordinary and partial differential equations have been proposed and successfully applied, little has been done so far for variational inequalities. On the basis of recent analytical results and previous work of the author, a predictor-corrector combination is proposed for a class of obstacle problems which exhibit fold points on the variational inequality branch. Numerical results for the Bratu problem are presented and verify the effectiveness of the method which may be increased further by, for example, combining it with multigrid techniques.