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Questions tagged [weak-solution]

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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
147 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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73 views

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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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 ...
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1answer
157 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
429 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
3k 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?