SYMMETRY REDUCTIONS AND A POSTERIORI FINITE ELEMENT ERROR ESTIMATORS FOR BIFURCATION PROBLEMS

Abstract

We discuss efficient continuation algorithms for solving nonlinear eigenvalue problems. First, we exploit the idea of symmetry reductions and discretize the problem on a symmetry cell by the finite element method. Then we incorporate the multigrid V-cycle scheme in the context of continuation method to trace solution branches of the discrete problems, where the preconditioned Lanczos method is used as the relaxation scheme. Next, we apply the symmetry reduction technique to the two-grid finite element discretization scheme [Chien & Jeng, 2005] to solve some nonlinear eigenvalue problems in physical science. The two-grid centered difference discretization scheme described therein was also implemented for comparison. Sample numerical results are reported.