Talk:Spectral element method

questionable statement
I cite: SEM, with fewer degrees of freedom per node,

I have the impression that the inverse is true: SEM has fewer nodes, but more degrees of freedom per node. J c stuifbergen 12:06, 4 September 2015 (UTC)

Merge?
Do not merge. The concepts are sufficiently distinct. Twbaroberts (talk) 21:30, 23 March 2010 (UTC)

This is a low quality article. I removed most of the stuff which was not quite right and what's left is a stub. I think it would probably be best to simply merge it into finite element method.

Loisel 05:50, 30 May 2007 (UTC)

Removed the statement: "The only relationship it has with the spectral method is its good convergence properties." It is related to the multidomain Chebyshev psuedospectral method, so I don't think this statement is true. —Preceding unsigned comment added by 146.151.113.182 (talk) 05:01, 2 May 2009 (UTC)

I think the problem is there is not agreement on what a spectral element method is. I agree that it is a finite element method, so it could be merged. Spectral elements implies high order, whereas to many people finite element implies low order. Specifically, it is a collocation finite element method. Collocation, pseudospectral, and differential quadrature methods are the same, so it is a finite element version of the pseudospectral method. I prefer the older traditional name collocation, which was adopted in 1938. I believe the name pseudospectral was introduced by Orzag in 1972. It creates confusion when these methods get renamed. There is also a differential quadrature element method. — Preceding unsigned comment added by TilTech (talk • contribs) 17:15, 28 April 2019 (UTC)

p-version and h-p version fem
Added a short note. But these would deserve their own article... Jmath666 (talk) 06:23, 11 December 2007 (UTC)

According to Lee (Spectral Element Method in Structural Dynamics, 2009, p. 6), spectral element method in a form that is presented by Patera 1984, is only a class of finite element method. In the spectral element method, as it is understood currently, the idea is to formulate problem in a frequency domain, solve it, and then transform it into time domain using inverse of FFT. In the current form, this article is low quality and should be merged(away). — Preceding unsigned comment added by 157.24.11.118 (talk) 14:56, 4 December 2012 (UTC)

Development History
The page states the original development of the method was by Patera (1984). That article considered only CGL points, whereas the method usually implies the use of LGL points, which was considered by Maday and Patera (1989). However, that method was described as early as 1977 by Young (see links below). The equivalent hybrid collocation Galerkin method, developed at Rice University (Diaz, Wheeler, Rachford), appeared first in 1975. The linear version of the method is noted in Strang and Fix (1973) and the quadratic version was developed by Gray in 1977 and Hennart in 1982. In 1986 Leyk developed the method in a reorganization of the hybrid collocation Galerkin method. Most of these developments were independent of each other. The development history is covered in a recent article (see below).

I want to make changes to correct some of the misinformation on this page, but want to give you a heads up.

1977 paper: https://www.researchgate.net/publication/284413721_A_preliminary_comparison_of_finite_element_methods_for_reservoir_simulation

1978/1983: https://www.researchgate.net/publication/236367847_A_finite_element_method_for_reservoir_simulation

2019 paper: https://www.sciencedirect.com/science/article/pii/S004578251830522X — Preceding unsigned comment added by TilTech (talk • contribs) 16:58, 28 April 2019 (UTC)

Related Methods
I have made some of the changes I mentioned in April. I was tempted to merge some of the "Related Methods", but instead left the others alone. I wanted state straight away that it is a FEM. The proliferation of names bothers me, because it contributes to confusion. I view two methods to be the same, when they give the same answer. That seems pretty simple, but others call methods different based on the form of the trial functions and so forth (nodal vs modal). I particularly have a problem with authors which come along and give a new name to an old method, so then you end up with two names and more confusion. pseudospectral and G-NI are two examples of renaming of old methods. — Preceding unsigned comment added by TilTech (talk • contribs) 21:36, 9 November 2019 (UTC)