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- W2088123313 abstract "A Legendre spectral Galerkin method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of two Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a preconditioned conjugate gradient method or the Cholesky method. The total cost of the algorithm is O(N3 ). Numerical results demonstrate the spectral convergence of the method." @default.
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- W2088123313 date "2001-01-01" @default.
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- W2088123313 title "A Legendre Spectral Galerkin Method for the Biharmonic Dirichlet Problem" @default.
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- W2088123313 doi "https://doi.org/10.1137/s1064827598342407" @default.
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