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== Disappointingly poor quality article ==
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::::While it is understandable that it could be seen that way, there are no separate approaches and there is no superiority of the variational approach as it is one and the same. It is the way chosen to present the topic that can lead to misuse and misinterpretation. I agree with your statement from the historical perspective and acknowledge that "The history of the method" section should describe how the method was originally implemented, the shortcomings of that original implementation and how it was given a full mathematical framework later on. The idea to pick a superior formulation is flawed since (as I said before) there is just one, however, from the point of view of the use and implementation of the method, there are several ways to get it wrong. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Snervi|Snervi]] ([[User talk:Snervi|talk]] • [[Special:Contributions/Snervi|contribs]]) 00:29, 30 November 2014 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->
:::::I still do not see why your overall description and the previous version cannot coexist. You need to provide published sources for any critique of what is in the original section. Simply asserting the superiority of your version is not enough. And continuing to revert other editors work is considered edit warring and can result in your be blocked for editing.--[[User:ArnoldReinhold|agr]] ([[User talk:ArnoldReinhold|talk]]) 05:22, 30 November 2014 (UTC)
== History ==
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::Five years later, and frankly, this article is still terrible. Guido's remark that one can only recognize the method at all from this article with great difficulty is spot-on. There are plenty of very intelligent people discussing the most banal of things on this discussion page - the "underlooked role" of one person or another in its history, etc. - can't we improve this article so that it is worth something? The article is terrible, folks, absolutely terrible. If making little changes is not going to improve the situation, then please, someone be bold and rewrite the whole thing. -[[Special:Contributions/24.13.162.248|24.13.162.248]] ([[User talk:24.13.162.248|talk]]) 00:59, 23 September 2010 (UTC)
:::What are you waiting for? Go ahead, make improvements if you have the ability (but please spare us with your opinion on how incapable all other editors are)! [[User:Tomeasy|<span style="color:#0000f1;font-family:Papyrus;cursor:help">'''''T<
== Not much use to a non-mathematician ==
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At the end of the day, it is still not correct to say that finite difference method is a type of finite element. The finite difference method has its own derivations, its own analysis, and its own proofs of convergence. At most, you can say that a large classes of problems that can be solved with finite difference can also be solved in a finite element framework. And even this statement would need some good references. [[User:Art187|Art187]] did provide some examples above, but a statement of such generality would need good references to back it up. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 16:10, 8 July 2008 (UTC)
: The book ''Numerical Methods for Partial Differential Equations'' By G. Evans, J. Blackledge, P. Yardley has its 4 chapters on FDM before introducing FEMs in chapter 5. So it might a good source to use here. I haven't actually read this article, and I'm probably not going to do that anytime soon... because even shorter ones on these topics are pretty badly written around here. [[User:Some1Redirects4You|Some1Redirects4You]] ([[User talk:Some1Redirects4You|talk]]) 16:07, 27 April 2015 (UTC)
== Issues with the rewrite ==
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::::: Endashes are the WP house style. [[Runge-Kutta]] and [[Navier-Stokes]] (hypen links) redirect to articles with endash between the names. [[User:Glrx|Glrx]] ([[User talk:Glrx|talk]]) 21:26, 8 February 2014 (UTC)
:::::: I agree that this a matter of debate, it basically depends on the most common usage. Another example, "short circuit" and "short-circuit". [[Special:Contributions/137.132.22.191|137.132.22.191]] ([[User talk:137.132.22.191|talk]]) 03:20, 19 February 2014 (UTC)
I agree with Mark Viking on this. I haven't seen this term hyphenated much in the literature. The people who spend their time enforcing some imaginary laws of [[Linguistic prescription|prescriptive]] English... should probably find something else to do. [[User:Some1Redirects4You|Some1Redirects4You]] ([[User talk:Some1Redirects4You|talk]]) 16:04, 27 April 2015 (UTC)
==Solution to a few Complexity Concerns and a suggestion on algos==
As you can see from my user name, I teach PDE's online, in many flavors. The comments on this talk page range from complimentary to outright hostile regarding the complexity level and quality of this article, lots of emotion about math, wow. Since I teach both undergrads and graduate engineers, let me suggest a solution for folks finding this too much or too tough: 1. Schaum's Outline of Finite Element Analysis is a great starting point for those who get lost at a beginning stage. Although FEA is a simple reductionist framework, implementation can involve hundreds of thousands of PDEs, some of which we run on supercomputers, and proofs and derivations are tough. 2. Once you get beyond the basics of proofs and the math, you'll be into algorithms immediately. Dover's 700 page book (The Finite Element Method) for $30 US is a great "next step" -- it is by Thomas J.R. Hughes, and goes from basics to advanced algorithm design (my field). It, however, is grad level and requires facility in PDEs and LP as a background. This is all to help frustrated Wiki editors and visitors, but to stay true to the talk page intent, I'd also like to humbly suggest that a section on algorithms might be warranted. I'd write it, but given the comments here, want to be sure there is at least some consensus that it is worth it. My reasoning is that although the proofs and derivations can get very difficult, the algorithmic designs are simple and elegant in many cases, and just crunch away at those PDEs! Frankly, this is more the reality today in practical solutions with Autocad, matlab, julia and even haskell, and users often don't have to know the full polygon story running beneath. In fact, many current interfaces allow you to drag and drop splines and beziers, OR write your own code in a little drop down command prompt box, OR do both! I would also like to thank the many contributors to this article, because, regardless of your opinion or feelings, it IS a lot of work! [[User:Pdecalculus|Pdecalculus]] ([[User talk:Pdecalculus|talk]]) 14:57, 30 March 2016 (UTC)
== FEM and FEA -- not exactly synonyms ==
I'm noticing that Finite Element Method and Finite Element Analysis are treated a synonyms in the introduction chapter. Though, "method" and "analysis" don't sound like the same thing to me at all. The way I have learned to understand it, FEM means the way calculations are done to perform FEA.
FEA is the larger context that includes first setting up a model of a practical case, then computing the numbers and finally interpretting the results of into events in the real world (often with recommendations of action).
FEM only means the technical part, essentially chopping the original problem into simpler parts whose behavior is "known" and constructing the bigger picture based on the interaction of all the simple elements. That alone is not yet an analysis.
The reason I wish to point this out is, that even very skilled and experienced people, who use these terms, some times seem unsure of, which to use and why, especially if they are not exactly in the business themselves -- say managing larger development projects, but with their background on a different field of technology. (Saw that happen just today ... again.)
A typical FEA, for example in the case of structural analysis may contain several runs in FEM, with different load cases and alternative structural or material build-ups. The results may contain information on mechanical durability, stability, response to vibration ... and for example a recommendation of a materials set to use.
So, if everybody agrees, that FEM and FEA are not synonyms, I'd be happy if somebody could take the effort of fitting a short explanation in the beginning of the introduction without breaking, what already is in there. :)
[[User:Peteihis|Peteihis]] ([[User talk:Peteihis|talk]]) 20:02, 21 May 2018 (UTC)
:I'm not sure everybody would make a distinction like that, but it sounds reasonable enough. May I suggest you add some words about this yourself? −[[User:Woodstone|Woodstone]] ([[User talk:Woodstone|talk]]) 08:00, 23 May 2018 (UTC)
:OK -- I might. Trying to keep it simple. :) [[User:Peteihis|Peteihis]] ([[User talk:Peteihis|talk]]) 06:07, 30 June 2018 (UTC)
:...And done. -- So basically the idea is that FEM is the tool and FEA is the job done using the tool. [[User:Peteihis|Peteihis]] ([[User talk:Peteihis|talk]]) 06:33, 30 June 2018 (UTC)
== Double derivative speak... ==
Sorry, but I am trying to understand what is meant in the section 'Weak formation of p1' when it states that 'if u solves P1...' I mean didn't the problem statement for P1 just declare that u” solves P1? Isn't u related but potentially quite different from u”? So what does that statement mean, 'if u solves P1...'
Maybe I just need to think about what that means. <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/134.137.180.129|134.137.180.129]] ([[User talk:134.137.180.129#top|talk]]) 19:15, 13 July 2018 (UTC)</small> <!--Autosigned by SineBot-->
== The article is one of the best introduction to finite element method . But the use of greens identities is not clear. we are in plane the weak formulation of p2 be derived more explicitly. in P1 use of mean value theorem be made explicit. ==
the article is one of the best introduction.But in weak formulation of p2 the grrens identity is not clear. we are ina plane region. explicit derivation be done.
in p1 use of mean value theorem be dmade explicit. Also the approach of distribution via sequential convergence and distributional derivative can be indicated in few lines.
on the contary tooo much space is used for h and the denedence on h. tthe whole can be summarized in h as the diameter of the traingle maximum amongst all traingles thas all very simple notion.
Further use of space H H be made clear. why not take H as space of continuous and differentiable except at finitely many points and make matters simple.
use of riesz representation be explicit write the functional and how to express it as inner product with u by RRT. excellent ouline which can be rigorous proof if we restrict H to be a suitable space.
please avoid lengthy discussions on h and subdivisions can be understood intuitively. But solve an explict one dime problem completely .
Also use of Gallerkin is not made explicit . please make that use explicit in the problem.
if these changes are done this can be most seductive logical introduction to fem . no good succint explnation exists on NET <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Anilped|Anilped]] ([[User talk:Anilped#top|talk]] • [[Special:Contributions/Anilped|contribs]]) 06:44, 1 June 2020 (UTC)</small> <!--Autosigned by SineBot-->
== Request for source/footnote ==
[[User:John Smith Anderson|John Smith Anderson]] ([[User talk:John Smith Anderson|talk]]) 11:59, 14 June 2020 (UTC)Under the heading "The weak form of P1" it is stated that the weak form implies the strong form. i.e. the equation above the line "The proof is easier for twice continuously differentiable u (mean value theorem)"
I cannot find a reference anywhere to a proof of this result. I am interested in a reference to a proof of this result, and I think it will improve the article for future readers who (like me) wonder how this result is proved. [[User:John Smith Anderson|John Smith Anderson]] ([[User talk:John Smith Anderson|talk]]) 11:59, 14 June 2020 (UTC)
:This is essentially Problem 1.1 in "Numerical Solution of Partial Differential Equations by the Finite Element Method" by Claes Johnson. (1) implies that u"-f is orthogonal to any v. Pick any point x inside the interval and restrict v to have support in delta-neighborhood of x. By the mean value theorem for integrals, there is a point c in that delta-neighborhood such that (u"-f)v is zero at c, i.e. such that (u"-f)(c)=0. Now by continuity (u"-f)(x)=0 which implies P1 since x was arbitrary. [[User:Tzanio|Tzanio]] ([[User talk:Tzanio|talk]]) 03:01, 10 July 2020 (UTC)
== Crystal plasticity FEM ==
Franz Roters is not the progenitor of CPFEM it existed long before he even had a PhD. He is, though, involved in the on-going development of DAMASK which is a crystal plasticity software package. [[Special:Contributions/2601:940:C081:4980:E3F1:FD00:EBB0:B69E|2601:940:C081:4980:E3F1:FD00:EBB0:B69E]] ([[User talk:2601:940:C081:4980:E3F1:FD00:EBB0:B69E|talk]]) 00:35, 15 December 2022 (UTC)
== No mention of element types? ==
The article currently doesn't mention (at least explicitly) a lot of element types (e.g. CST, LST, Isoparametric, etc)....should it? Or is the intent to not get quite that deep? (I.e. just a general overview of the method.)[[User:Rja13ww33|Rja13ww33]] ([[User talk:Rja13ww33|talk]]) 16:45, 2 May 2025 (UTC)
:By the way, any suggestion for a source for element pics (that wouldn't be a copyright violation) would be welcome. Everything I can think of would create copyright problems. [[User:Rja13ww33|Rja13ww33]] ([[User talk:Rja13ww33|talk]]) 00:38, 20 May 2025 (UTC)
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