Abstract

Solving the biharmonic eigenproblem by the finite element method M.D. Mihajlovic We present the computational results concerning the spectral properties of the biharmonic operator on various two-dimensional domains. We focus our attention to the behaviour of the least biharmonic eigenfunctions near sufficiently small corners since it is known that they have an unbounded number of oscillations. We present the results which demonstrate that a number of these sign changes may be accurately computed using an unstructured finite element solver. We also present the numerical results which relate to the parity change in the least biharmonic eigenfunction when considered on a family of symmetric and non-convex domains. These results support some new conjectures on the behaviour of the biharmonic operator. This report presents a joint work with B.M. Brown (Cardiff University), E.B. Davies (King's College London), and P.K. Jimack (University of Leeds).

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