Lyashko, A. D.; Solov’yev, S. I. Fourier method of solution of FE systems with Hermite elements for Poisson equation. (English) Zbl 0816.65079 Sov. J. Numer. Anal. Math. Model. 6, No. 2, 121-129 (1991). 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. Cited in 13 Documents 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 Keywords:finite element; Poisson equation; direct algorithm; block elimination; method of separation of variables; discrete fast Fourier transform PDFBibTeX XMLCite \textit{A. D. Lyashko} and \textit{S. I. Solov'yev}, Sov. J. Numer. Anal. Math. Model. 6, No. 2, 121--129 (1991; Zbl 0816.65079)