Finite element eigenvalues for the Laplacian over an L-shaped domain
A finite element method is described which determines determined the eigenvalues for Laplaces equation on an L-shaped region. The numerical method uses an expansion near the internal corner with angle \(3\pi\) /2 and matches it via a transition layer of elements to a standard bilinear approximation in the region away from the corner. Adequately accurate eigenvalues are obtained compared to previous results. The current method is of more general applicability, than those previously described and could incorporated into standard finite element codes.
scientific article; zbMATH DE number 4050911