Questions tagged [weak-solution]
The weak-solution tag has no usage guidance.
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0answers
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Constraining the total volume in Finite Element Methods
I have a diffusion problem which can be broken down to be:
$-\Delta u = f(u) $ on $\Omega ~/~ \Omega_{int}$
$u = 1$ on $\Omega_{int}$
Note that this is an internal Dirichlet constraint to the ...
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1answer
129 views
Unphysical Behaviour Characteristic-Wise WENO5-Z
I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and ...
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1answer
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Deriving weak form of a set of scalar equations
I have the equilibrium equation in elasticity for a static case.i.e
Div T=0.
For certain implementation, I have to get the x and y component equations and then derive the weak form separately. How is ...
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0answers
34 views
How do 'virtual kinematics/functions' play a role during deriving weak form formulations for physical problems?
I wanna ask a question that confuses me quite a long time. I saw many guys, in the context of computational mechanics, they seemed to choose the virtual functions or kinematics in a way that some ...
0
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1answer
144 views
Ritz, Galerkin, Weak Form, FEM: How to catch up the basics? [duplicate]
I have to deal with FEM and the numerical solution of PDEs a lot. While I'm doing ok when just applying or implementing it, I observe a lack of understanding when authors begin to argue with "Ritz", "...
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2answers
357 views
FEM: Obtaining the Weak Form
In the the Finite Element Method (FEM), we attempt to obtain the Weak Form of the described equation. I understand that this is an attempt to reduce the order regularity of the equation, but what are ...
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1answer
2k views
Strong vs. weak solutions of PDEs
The strong form of a PDE requires that the unknown solution belongs in $H^2$. But the weak form requires only that the unknown solution belongs in $H^1$.
How do you reconcile this?
