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- Petter E. Bjørstad, Bjørn Peter Tjøstheim
- SIAM J. Scientific Computing
- 1997

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)

- Petter E. Bjørstad, Bjørn Peter Tjøstheim
- Computing
- 1999

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)

Gas coning is a tendency of the gas to impel the oil downward in an inverse cone contour toward the well perforations. Once the gas reaches the well, gas production will dominate the well flow and the oil production will hence significantly decrease. From an economical and operational standpoint this condition is undesirable since the gas price is much… (More)

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