We propose a new finite element approach, which is different from the classic Babuska-Osborn theory, for some nonlinear eigenvalue problems. The eigenvalue problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. Finite element methods are used for discretization. The convergence of eigenvalues/eigenvectors is proved using the abstract approximation theory for holomorphic operator functions. Then the spectral indicator method is extended to compute the eigenvalues/eigenvectors. Two nonlinear eigenvalue problems are treated using the proposed approach.
Time: October 9, 2020 2:30pm-3:30pm
Location: Virtually via Zoom
Host: Qi Wang