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Fourier method of solution of FE systems with Hermite elements for Poisson equation. (English) Zbl 0816.65079

Summary: A finite element (FE) system with bicubic Hermite basis functions is considered for the Poisson equation in the rectangular domain. To solve the system of linear equations with respect to the nodal parameters of this FE system, the paper suggests a direct algorithm making use of block elimination of unknowns and the method of separation of variables with the discrete fast Fourier transform.
The method obtained in the paper asymptotically has the same computational cost as the method of separation of variables with the discrete fast Fourier transform in the case of the simplest finite difference approximation of the Poisson equation in the rectangular domain.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F05 Direct numerical methods for linear systems and matrix inversion
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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