Finite dimensional approximation of two-parameter nonlinear problems

Summary. In this paper we study a general theory for the numerical approximation of functional nonlinear two-parameter problems in a neighbourhood of an isola center. The results are also valid for a certain class of perturbed bifurcation points. The abstract theory is applied to the Galerkin approximation of nonlinear variational posed problems. In this case, as a consequence of the error being orthogonal to the approximating space, we prove the superconvergence of the perturbation parameter, whereas for the bifurcation parameter and the solution we obtain the same order as in the linear problem. Numerical results are given for the one-dimensional Brussellator model. Received June 10, 1992 / Revised version received May 16, 1994