Computational Galerkin Methods

By C. Fletcher. 1983

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks (2001, methodology): “[3], Fletcher [4], Hughes [5], Reddy and Gartling [6], Zienkiewicz and Taylor [7]) and the finite volume method (FVM)”
The Fokker-Planck Equation (2010, methodology): “For a greater detail, an authoritative book, computational Galerkin methods, authored by C A J Fletcher can be consulted (Fletcher 1984).”
The numerical solution of linear ordinary differential equations by feedforward neural networks (1994, methodology): “The various subclasses of the method of weighted residuals are discussed and compared at great length by Finlayson [16] and Fletcher [18].”
On Low-Dimensional Galerkin Models for Fluid Flow (2000, methodology): “A standard technique to find such a system of ODEs is the method of Galerkin projection [ 6 ].”
Modeling of distributed parameter systems for applications—A synthesized review from time–space separation (2010, unknown): “Because the fastmodes contribute little to the whole system, only the first n slow modes in the expansion will be retained in practice [23]”
Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load (2012, unknown): “The Galerkin truncation method is used to discretize the system and the series expansion form when y(x,t) is assumed as [34] yðx,tÞ 1⁄4 X1 k 1⁄4 1 qkðtÞfkðxÞ (9)”
Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation (2013, methodology): “(2.4) In the traditional Galerkin method, the trial basis is equal to the test basis; vi ≡ ui (Fletcher 1984).”
Low-order Control-relevant Models for A Class of Distributed Parameter Systems (2001, methodology): “Since the projection functions and the basis functions are from the same set (see Equation (2.6)), this projection method is also called Galerkin’s method [ 21 , 38].”
Solutions of differential equations in a Bernstein polynomial basis (2007, methodology): “Many authors such as Bottcher and Strayer [2] applied the B splines to time-dependent problems, Johnson and co-workers to many-body perturbation theory [7,8] Fischer and co-workers [3–5] to Hartree–Fock calculations and continuum problems.”
Approximate policy iteration: a survey and some new methods (2011, background): “Note that the projected equation framework has a long history in the context of Galerkin methods for the approximate solution of high-dimensional or infinite-dimensional linear equations (partial differential, integral, inverse problems, etc. See, e.g., references [37, 38 ]).”