Unformatted text preview: Note that as the eigenvalue increases, the number of oscillations in the eigenfunction increases. In order to capture this behavior in a piecewise linear approximation, we need a Fner mesh for the eigenfunctions corresponding to larger eigenvalues than we do for those corresponding to smaller eigenvalues. (b) When using piecewise linear Fnite elements, the j th computed eigenvalue lies in an interval [ λ j , λ j + C j h 2 ], where h is the mesh size used in the triangulation. This is observed in our computation using the program problem1b.m , found on the website. The error plots are shown in ±igure 31.2. The horizontal axis is the 187...
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- Fall '11
- Eigenvalues, Eigenvalue, eigenvector and eigenspace, Eigenfunction, Wm, Simple Eigenvalues, larger eigenvalues