| Abstract: | In this paper, we study the order reduced finite element method for thefourth order eigenvalue problems on multi-connected planar domains. Particularly,we take the biharmonic and the Helmholtz transmission eigenvalue problems asmodel problems, present for each an equivalent order reduced formulation anda corresponding stable discretization scheme, and present rigorous theoretical analysis. The schemes are readily fit for multilevel correction algorithms with optimalcomputational costs. Numerical experiments are given for verifications. |
