Obtaining the boundary data of a solution

[Turiya Soham]

Hi all,

I have just started in dealii and going through the tutorials to solve a Neumann boundary value problem. 

I have the following situation: the Neumann boundary data (say g) is defined as a Function and the  solution obtained by solving my pde is a Vector<double> (say v). How do I take the L2 inner product of g and trace(v). How do I get this inner product between a Function and a Vector <double>.

I can find each face which is on the boundary and I can get the values of g at all the

quadrature points of the face and the JxW at those points. However, to obtain the

surface intergral, I also need the values of v at these quadrature points. How can I get

the values at the quadrature points of the solution v?

Thank you,

[Wolfgang Bangerth]

Turiya,

Your inner product is, I assume, an integral over the boundary. Boundary
integrals are always computed via the FEFaceValues class, in the same way as
integrals over cells are computed via the FEValues class.

To get the solution values at quadrature points you would use the
FEFaceValues::get_function_values() function. This is no different than what
FEValues::get_function_values() does for quadrature points on cells, which is
something you can find in a number of tutorial programs (e.g., step-9,
step-21, or step-15's and step-19's use of the corresponding
get_function_gradients() function).

Best
W.


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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Turiya Soham]

Dear Prof. Bangerth,

Thank you. I checked this on my problem and it is working.

Regards,