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

Figure 3

Convergence in the first ten eigenvalues for each of the four cases in Section 4.1: (a) unit square and fixed edges; (b) unit square and one free edge; (c) unit disk and fixed boundary; (d) unit disk and free boundary (with zero eigenvalues omitted). In all cases, the dashed line for fourth-order convergence is shown for comparison. denotes the number of points used to discretize the overall two-dimensional geometry in each case.

(a)

(b)

(c)

(d)