iMechanica - Comments for "Meaning of Weak form use in Finite element Method"
https://imechanica.org/node/13788
Comments for "Meaning of Weak form use in Finite element Method"enI really appreciate this
https://imechanica.org/comment/27387#comment-27387
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<p><em>In reply to <a href="https://imechanica.org/node/13788">Meaning of Weak form use in Finite element Method</a></em></p>
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</ul>Tue, 30 Jun 2015 08:16:20 +0000jesonkocomment 27387 at https://imechanica.orgstrong form: PDE form.
https://imechanica.org/comment/26567#comment-26567
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<p><em>In reply to <a href="https://imechanica.org/node/13788">Meaning of Weak form use in Finite element Method</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>strong form: PDE form.</p>
<p>weak form: integration form, which can be obtained by weighted integration of the PDE and then using integration by part. </p>
<p>why PDE is "strong" form and integration form is "weak form"? because for example the PDE is 1-d Poisson, i.e. -u''=f. then to make sense of the term -u'' in traditional sense, function u should belong to C2 function space, while f belongs to c0. the integration counterpart of -u''=f is int(u'*v'-f*v)=0, to make sense of the integration term in(u'*v') we need select functions u and v from function space H1. to make sense of int(f*v) we need to select f from L2, or more larger space H^-1. Because the function space H1 required for u in integration form is larger than function space L2 required for u in PDE form, so we say the integration form is weak form and PDE form is strong form. Actually, the integration form relaxes the regularity (smoothness) requirement of the unknown function u, which is the reason it's called weak form. In the other hand, the regularity requirement for u in PDE is too strong for real world engineering problems, such as problems with sharp geometry change, the integration form is more suitable for real world engineering problems.</p>
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<p>The above is my understanding the definition of "strong form" against "weak form". </p>
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</ul>Thu, 13 Nov 2014 21:22:53 +0000Junwei Xingcomment 26567 at https://imechanica.orgTest Function
https://imechanica.org/comment/23946#comment-23946
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<p><em>In reply to <a href="https://imechanica.org/node/13788">Meaning of Weak form use in Finite element Method</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
A Test Function in Weighted Residuals is not the Exact Solution It is an Approximation of the Exact and is Intuitivly assumed.
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In some cases it can Fit the Exact. With Galekine Method it Leads to the Finite Element Formulation.
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M.L.
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</ul>Sat, 12 Jan 2013 10:41:33 +0000mohamedlaminecomment 23946 at https://imechanica.orgThnaks for reply. I will
https://imechanica.org/comment/23944#comment-23944
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<p><em>In reply to <a href="https://imechanica.org/comment/22604#comment-22604">For more understanding on</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Thnaks for reply. I will study it.</p>
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</ul>Fri, 11 Jan 2013 23:10:28 +0000rohan_patel8388comment 23944 at https://imechanica.orgFor more understanding on
https://imechanica.org/comment/22604#comment-22604
<a id="comment-22604"></a>
<p><em>In reply to <a href="https://imechanica.org/node/13788">Meaning of Weak form use in Finite element Method</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
For more understanding on these, read these books:
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Chapter 3: Fundamentals of Finite Element Method (Vol I) by ZienKiewicz & Taylor -> very elaborate
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Chapter 3: Concepts and Application of Finite Element Analysis, by Cook ->short but sweet...to the point :)
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The world started with 0, is progressing with 0, but doesn't want 0.
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</ul>Wed, 05 Dec 2012 04:38:07 +0000Akumarcomment 22604 at https://imechanica.orgWeak form means, instead of
https://imechanica.org/comment/22603#comment-22603
<a id="comment-22603"></a>
<p><em>In reply to <a href="https://imechanica.org/node/13788">Meaning of Weak form use in Finite element Method</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Weak form means, instead of solving a differential equation of the underlying problem, an integral function is solved. The integral function implicitly contains the differential equations, however it's a lot easier to solve an integral function than to solve a differential function. Also, the differential equation of system poses conditions that must be satisfied by the solution (hence called STRONG form), whereas, the integral equation states that those conditions need to be satisfied in an average sense (hence WEAK form). However, do not understimate the power of integral functions just by its name "weak form".
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An example is stresses on free surface. Strong form says if there is no traction on the surface, corresponding stresses must be zero.So if we can solve the PDE, we'll get exact zero stresses. But all FEA code will give you some stress on the surface since whole FEA is based on integral functions. So as you refine the mesh, the stress value at traction free surface goes closer and closer to zero...this is average sense :)
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The world started with 0, is progressing with 0, but doesn't want 0.
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</ul>Wed, 05 Dec 2012 04:26:48 +0000Akumarcomment 22603 at https://imechanica.org