A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains

Figure 7

Convergence in the first 5 eigenvalues for the smoothed L-shaped membrane () is roughly 4th order when compared to the finest discretization tested (). Note that the eigenvalues do not necessarily converge to those of the true L-shaped membrane with a sharp corner due to the approximation of the corner geometry. For example, here when , even though (e.g., [2, 4]) for the membrane with the sharp corner.