[Dune] Geometric position of dofs

[Nicolas Schwenck]

I am trying to implement an extended finite element approach, where you
can have discontinuities of the solution within elements. This is
reached by discontinuous basis functions. This discontinuity is reached
by multiplication of the basis functions by (H_qp - H_dof). Here H are
"jumping" functions. They depend on the geometric position of the
quadrature point (the dof respectively) to the discontinuity-"line" (on
the same side/on the other side). Therefore it is necessary for me to
know, where the dofs are positioned.

In more detail: you have the geometric cut of the discontinuity line
through the element. Then you check whether each dof is "on the left" or
"on the right" hand side of the line. According to this the step
functions H_dof(x of the dof) (associated to the dofs) have a different
value. The quadrature point is the geometric point, where the
basis/test-functions are evaluated. The same is done for each quadrature
point (is it on the left or on the right), H_qp(x of the qp).

For the first approach I will go with just simple Q1 "normal" finite
elements and use the corner function to determine the position of my
dofs. Maybe I try to generalize my approach later and come back then to
the hints you send me.

Thank you again, kind regards, Nicolas

> Am 10.08.2010 14:42, schrieb Nicolas Schwenck:
>   
>> Dear Dune,
>>
>> Is there an easy way to get the geometric position of each degree of
>> freedom in each element (it depends on the used elements, e.g. Q, RT,
>> etc., and the element order, i.e. the specific finite element map)
>> within the user-written local operator?
>>
>> Thank you in advance. Kind regards, Nicolas
>>
>>     


-- 
_____________________________________________________________________

Dipl.-Ing. Nicolas Schwenck

IWS, Universität Stuttgart 		     phone: +49 711 685 64736
Pfaffenwaldring 61			     fax:   +49 711 685 60430
D-70569 Stuttgart

            email: nicolas.schwenck at iws.uni-stuttgart.de
                url: www.hydrosys.uni-stuttgart.de
_____________________________________________________________________