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Re: [Getfem-users] Dirichlet condition

From: Yves Renard
Subject: Re: [Getfem-users] Dirichlet condition
Date: Tue, 14 Jul 2015 10:28:26 +0200 (CEST)

Dear Aaron Oaks,

In that example, the Dirichlet data is defined on mf_ue which is in fact not a 
finite element space, it is defined to span a certain number of global 
functions. So that the Dirichlet Data is a particular linear combination of 
these global functions.

Of course, it is not possible to prescribe it exactly on the unknow which is 
define on an enriched finite element space. So, here, the Dirichlet condition 
is prescribed with a penalization technique. This means that a term
\int_{\Gamma} (u - Dirichlet_data) * gamma * Test_u
is added to the formulation, with gamma a penalization parameter (1e12 here).

Another possibility would be to prescribe the Dirichlet condition with a 
Lagrange multiplier or with Nitsche's method.

Best regards,


----- Original Message -----
From: "Oaks, Aaron Jameson" <address@hidden>
To: "getfem-users" <address@hidden>
Sent: Monday, July 13, 2015 9:01:20 PM
Subject: [Getfem-users] Dirichlet condition


I am a PhD student at University of Illinois and I'm starting in on a project 
studying crack propagation. I'm just starting out with GetFEM++ and FEM in 
general, so I apologize if this question is remedial. I went through the 
thermo-elastic and electrical coupling tutorial on the website, and that went 
well, but going through the example I'm having trouble seeing how 
the Dirichlet BC is assigned. In the coupled tutorial I understood how it 
worked using either a constant value or values interpolated on the same MeshFem 
for each boundary node, but with all the different MeshFems in different bases 
defined to accommodate the crack I seem to be at a loss. Could I get a 
mathematical description of the Dirichlet condition to be assigned, and an 
explanation of how the example code goes about assigning that condition? Thank 
you very much for your time. 

Aaron Oaks 

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