Talk:Finite element method

message: This is a fine example of an article that represents the worst of all worlds - it fails to accurately present either the mathematical, physical or engineering aspects of FEM. It is overly simplified for applied mathematicians, incomprehensible for lay persons and useless for the practicing engineer/analyst. There are numerous blatantly incorrect / misleading statements and glaring errors of omission, and the level of presentation alternates between sophomoric and overly pedantic. Students and laymen would be well advised not to attempt to learn anything from this article!
:Judging by this discussion page, you are not the only one who is disappointed in the quality of this article. I myself have an engineering background, and even a very good working knowledge of numerical methods, and I must say, I feel exactly how you do about this article. I really have no idea what type of audience it's supposed to be targeted at. Certainly, the FEM is vastly too technical and abstruse for the general population, but it is of considerable interest to many scientific and engineering professionals. Hence, this article ought to be targeted at individuals who are well-versed in linear algebra, calculus, and are looking to enhance their practical understanding of the more advanced numerical methods like FEM. The current article reads like it was written by a mathematics graduate student, rambling about what he has read in his textbooks. At the risk of being cruel to those who have put forth an honest effort to improve it, several years after the first complaints were lodged, this remains one of the worst articles on Wikipedia I have ever read. I think the whole thing needs to be rewritten. -24.13.162.248 (talk) 00:53, 23 September 2010 (UTC)
replies: text: I find myself in complete agreement with the two above statements. I humbly suggest that this page be split up into multiple independent pages on the subject from the differing perspectives that would make use of this subject matter (mathematicians, physicists, engineers...) so that all three of those groups could have a page replete with useful information without the current requisite diversions into other fields' terminology and conventions. Put simply, this topic is far too large for one page fully describe the scope of. Bobxii (talk) 17:50, 9 November 2010 (UTC)
replies: text: Acknowledging that no extensive additions or rewrites have been performed since the last such comments of criticism have been posted, I have to disagree with them. In fact, reading this article has been one of my most helpful Wikipedia visits so far. While I agree that there are omissions and phrasings that need correction, and without commenting on what might be deemed missing, I strongly disagree with the opinion that what is written in the article now is such a complete disaster. In fact, after I have checked out several introductory online materials on the topic, and even a few book previews on Amazon, I must say that this here is the only article on the topic that helped me understand. It defines a goal, it states prerequisites, it sets a foundation and builds from there, while explaining why each step is taken. A task that all other resources I consulted utterly failed at. I am moderately educated in mathematics, I am not a technical engineer. I'm not able to follow so-called introductions that don't manage to present even one full sentence of context before hitting me over with 50 formulae. After this Wiki article, I understand the principle, and can even implement finite element methods, or at least know what to look for if I come upon a problem. If the community thinks this article is in need of such a major overhaul, so be it, but consider not destroying these qualities of the article in the process. Solving stiff PDEs is not a problem limited to only the most high-level professionals with engineering degrees. 89.217.175.204 (talk) 00:04, 20 January 2011 (UTC)

text: I don't see why the paragraphs you say were written by Barna Szabo and Mark Ainsworth can't be added rather than have to replace what was there. They seem complementary to me.--agr (talk) 02:27, 28 November 2014 (UTC)
replies: text: Unfortunately, the previous text could not be edited because it started from the wrong premise. There were misleading statements on the nature of the Finite Element Method that come from constructing the idea of the method (and terminology) from the element up, when it should be the other way around, arriving to the element formulation after formulating a  variational problem and a discretization strategy. The element based approach, used by early investigators, is now considered obsolete. It has hindered the understanding of what a finite element method is.  — Preceding unsigned comment added by Snervi (talk • contribs) 22:39, 29 November 2014 (UTC)
replies: text: As this reference makes clear, both approaches are still taught and used: http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/IFEM.Ch01.d/IFEM.Ch01.pdf Wikipedia tries to present different approaches to a subject as long as they are supported by reliable sources, not pick the best one. If you have published reliable sources for your claims of the superiority of the variational viewpoint, the article can be structured to say something like, "Historically FEM was viewed as blah blah blah,. A more modern approach is blah blah blah, which as the following benefits..."--agr (talk) 23:26, 29 November 2014 (UTC)
replies: text: 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.  — Preceding unsigned comment added by Snervi (talk • contribs) 00:29, 30 November 2014 (UTC)
replies: text: 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.--agr (talk) 05:22, 30 November 2014 (UTC)
thread_title:  Disappointingly poor quality article 

message: How about John Argyris' contribution? I think there should be a relevant revision in the history section, provided that experts in the field also agree. 
One short biography appears here: http://www.cimne.upc.es/webcimne/boletinECCOMAS/20040518.htm in word format. I do not know though if it can be made available to wikipedia...
http://www.mlahanas.de/Greeks/new/Argyris.htm
Dpser 17:57, 16 January 2007 (UTC)
thread_title:  History 

message: There is also something not clear about how the integration by parts is actually done. Something was left out there. (BTW does this have anything to do with Lu=g being of the Sturm-Liouville type?)
--
No. When the operator is not Hermitian, there is still a bilinear form, except of course that it is not an inner product. One can obtain existence and uniqueness from the Lax-Milgram theorem, assuming that the bilinear form is coercive. If it is not, it is sometimes still possible to obtain a form of the Fredholm alternative.
When L is of the Sturm-Liouville type, the Dirichlet problem gives rise to a Hermitian operator and so the theory is nicer (and the linear solve is also easier -- conjugate gradient with a preconditionner can often be used.) If the boundary condition is not Dirichlet, the bilinear form is usually not symmetric, even if L is of Sturm-Liouville type. Loisel 11:46, 26 Jul 2004 (UTC)
thread_title:  Sturm-Liouville? 

message: How to fit Finite element analysis in this article? --Abdull 16:30, 21 February 2006 (UTC)
replies: text: Finite element analysis involves the application of finite element methods to specific problems. Temur 23:40, 9 October 2007 (UTC)
thread_title:  Finite element analysis 

message: I think there should be a seperate article on the spectral/hp element method, which is NOT the same as the current spectral method article, as this FEM article only mentions SEM in passing and does not give ANY details
there is also no mention of testing functions, galerkin method, etc. also no references to fem textbooks. i will add those in when i get a chance --anon
: There is a Galerkin method article. I suggest you write more details here before making big changes to the article. Oleg Alexandrov (talk) 02:43, 30 June 2006 (UTC)
replies: text: Those are called 'higher order finite elements'. Temur 23:38, 9 October 2007 (UTC)
thread_title:  spectral element method 

message: Does the subject of finite element meshing deserve its own article?  I'm thinking so.  It's distinct enough from the computer graphics description. Ojcit 19:21, 2 October 2006 (UTC)
thread_title:  meshing 

message: Is the finite element method somehow related to the finite volume method ? —The preceding unsigned comment was added by Domitori (talk • contribs) 01:11, 17 December 2006 (UTC)
replies: text: They are both method of numerically approximating the solution to differential equations.  I'm not sure how the formulations might be similar beyond that. - EndingPop 15:12, 17 December 2006 (UTC)
replies: text: They both can be fit into Petrov-Galerkin approximation framework. You can think of Finite Volume Method as a FEM with special type of trial function spaces. Temur 23:37, 9 October 2007 (UTC)
thread_title:   [[finite element method]] and  [[finite volume method]] ? 

message: The section on how to choose the basis is in my opinion too much focused on triangles, since the FEM can be applied to general elements, for example also to quads etc.
: I would agree. It needs to be much more general. - EndingPop 17:11, 2 May 2007 (UTC)
thread_title:  triangles 

message: is referenced in the text, but I can't find it (should be somewhere between (2) and (4) I guess). --147.122.2.207 10:51, 26 January 2007 (UTC)
replies: text: Never mind, I think I found it. I have restored the tag. --147.122.2.207 10:54, 26 January 2007 (UTC)
thread_title:  equation (3) 

message: 6.29 (Domains of Finite Width) Consider the problem of determining for what domains \Omega in \mathbb{R}^n is the seminorm
:|u|_{m,p,\Omega} = \left( \sum_{|\alpha|=m} ||D^\alpha u||^p_{0,p,\Omega} \right) ^{1/p}
actually a norm on W_0^{m,p}(\Omega) equivalent to the standard norm [...]
We can easily show the equivalence of the above seminorm and norm for a domain of finite width, that is, a domain in \mathbb{R}^n that lies between two parallel planes of dimension (n-1). In particular, this is true for any bounded domain.
6.30 THEOREM (Poincaré's Inequality) If domain \Omega \subset \mathbb{R}^n has finite width, then there exists a constant K=K(p) such that for all \phi \in C_0^\infty(\Omega)
:||\phi||_{0,p,\Omega} \leq K |\phi|_{1,p,\Omega}.
[...]
6.31 COROLLARY If \Omega has finite width, |\cdot|_{m,p,\Omega} is a norm on W_0^{m,p}(\Omega) equivalent to the standard norm ||\cdot||_{m,p,\Omega}.
---
That said, the reason why I skipped this explanation in the text is that it would considerably lengthen the discussion and this is not really about finite elements, but rather, this is a fact about Sobolev spaces or Elliptic boundary value problems.
Loisel 18:22, 27 June 2007 (UTC)
replies: text: I just want to add that the counterexample 1 does not work since the function is not in H_0^1(0,1). Temur 23:34, 9 October 2007 (UTC)
thread_title:  An Equivalent Norm for $W_0^{m,p}(\Omega)$ 

message: So how many of these codes are we going to add to the page? Is there WP policy regarding this sort of thing, because I feel like this is getting out of hand. - EndingPop (talk) 16:38, 18 June 2008 (UTC)
thread_title:  Examples of FEM Codes 

message: In the current version of the article, the section "Outline of general mathematical framework" suggests that finite element problems are always solved in H^1_0 which is not right. Oleg Alexandrov (talk) 04:38, 8 July 2008 (UTC)
thread_title:  Issues with the rewrite 

message: this method is most important in engineering especially in CAE with software like ansys and abaqus. it should not be in physics.  —Preceding unsigned comment added by Saeed.Veradi (talk • contribs) 04:44, 20 July 2008 (UTC)
replies: text: I agree physics is not the most relevant category. I removed it. Oleg Alexandrov (talk) 02:37, 22 July 2008 (UTC)
thread_title:  Application of FEA 

message: The first point on the FDM was as follows
*The finite difference method is an approximation to the differential equation; the finite element method is an approximation to its solution.
Both methods are used to approximate the solution of a differential equation: that's what they are for. Although the author of the sentence probably has a good and well-established idea about both methods, this senence does not convey it. To me it sounds like: use FE if you want the solution of a differential equation. Use FDM if you want the differential equation itself. I hope we can agree that that is definitely not true.  —Preceding unsigned comment added by 130.89.67.43 (talk) 16:36, 22 April 2009 (UTC)
thread_title:  Removed Half-truth in the difference between FE and FDM 

message: The technical section of the article mentions variational form with a link to the calculus of variations.  The link is not appropriate because the linked page does not define variational form. Jfgrcar (talk) 22:29, 7 December 2010 (UTC)
thread_title:  Variational form 

message: I have a question about this method, for which I think the answer should be in the article (which it currently not as far as I can see). I wonder how the gradient and the Laplacian of the scalar field is calculated, after the discretization has been carried out? This is highly relevant to the article, since being able to calculate these two is necessary in order to be able to solve most PDE:s at all using the finite element method. --Kri (talk) 20:42, 6 April 2011 (UTC)
thread_title:  How is the gradient and the Laplacian calculated? 

message: 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! Pdecalculus (talk) 14:57, 30 March 2016 (UTC)
thread_title: Solution to a few Complexity Concerns and a suggestion on algos

message: 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. :)
Peteihis (talk) 20:02, 21 May 2018 (UTC)
replies: text: 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? −Woodstone (talk) 08:00, 23 May 2018 (UTC)

text: OK -- I might. Trying to keep it simple. :) Peteihis (talk) 06:07, 30 June 2018 (UTC)

text: ...And done. -- So basically the idea is that FEM is the tool and FEA is the job done using the tool. Peteihis (talk) 06:33, 30 June 2018 (UTC)
thread_title:  FEM and FEA -- not exactly synonyms  

message: 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.  — Preceding unsigned comment added by 134.137.180.129 (talk) 19:15, 13 July 2018 (UTC)
thread_title:  Double derivative speak... 

message: 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  — Preceding unsigned comment added by Anilped (talk • contribs) 06:44, 1 June 2020 (UTC)
thread_title:  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.   

message: John Smith Anderson (talk) 11:59, 14 June 2020 (UTC)
replies: text: 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. Tzanio (talk) 03:01, 10 July 2020 (UTC)
thread_title:  Request for source/footnote  

message: 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. 2601:940:C081:4980:E3F1:FD00:EBB0:B69E (talk) 00:35, 15 December 2022 (UTC)
thread_title:  Crystal plasticity FEM