[Getdp] Galerkin Equations

[Christophe Geuzaine]

Sebastian wrote:
> Hi all:
> 
> I am new here, and new in GetDP. And I have problems to understand
> the notation used in the Galerkin equations used in GetDP.
> 
> I think that I understand the first expression, but I don't known what to 
> do with the second expression.
> 
> As I understand if I have:
> Equation{
>    Galerkin { [ -nu[] * Dof { d a }, {d a } ];
> 		In Domain; .....
>    Galerkin{ [ hc[], { d a }];
> 		In Domain_M ,....
>    Galerkin{ [-js[], { a } ];
>   		In Domain_S , ...
> }
> 
> GetDP solves d a = ( js - hs ) / nu, the summation of the first expressions 
> = 0.
> But, What to do with the second expressions, in Galerkin definition?
> 
> Why put { da } in the first and second Galerkins, and why put { a } in the 
> third ?
> 

This comes from the weak formulation of the PDE: "Galerkin { [ hc[] , {d
a} ] }" means "\int hc[] \cdot d a", i.e., the integral of the inner
product of "hc[]" with "d a" over the domain, where "a" is a test function.

Have a look at any standard finite element textbook for an introduction
to weak formulations. (There are some references in the getdp wiki.)



> Thanks.
> 
> 
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> 


-- 
Christophe Geuzaine
Assistant Professor, Case Western Reserve University, Mathematics
http://www.case.edu/artsci/math/geuzaine