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This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of(More)
We show that one can derive an O(N 3) spectral-Galerkin method for fourth order (biharmonic type) elliptic equations based on the use of Chebyshev polynomials. The use of Chebyshev polynomials provides a fast transform between physical and spectral space which is advantageous when a sequence of problems must be solved e.g., as part of a nonlinear iteration.(More)
We solve the biharmonic eigenvalue problem $\Delta^2u = \lambda u$ and the buckling plate problem ${\Delta}^2u = - {\lambda}\Delta u$ on the unit square using a highly accurate spectral Legendre--Galerkin method. We study the nodal lines for the first eigenfunction near a corner for the two problems. Five sign changes are computed and the results show that(More)
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