[Getdp] Question

[michael.asam at infineon.com]

Hi Cristian,

the PDEs for GetDP have to be in weak form (see http://en.wikipedia.org/wiki/Weak_formulation).
The equation you mentioned (div(a grad(v)) = f) is in strong form and has to be
converted to the weak form before being implemented in GetDP. For more on this topic
please have a look at one of the books mentioned in the wiki (https://geuz.org/trac/getdp/wiki/TheoreticalReferences):
Understanding and Implementing the Finite Element Method - Mark S. Gockenbach - ISBN 978-0-898716-14-6
Numerical Methods in Scientific Computing - J. van Kan, A. Segal, F. Vermolen - ISBN 90-71301-50-8 - ​http://www.vssd.nl/hlf/a002.htm<http://www.vssd.nl/hlf/a002.htm>
Introduction to the Calculus of Variations - Jim Fischer: ​http://online.redwoods.cc.ca.us/instruct/darnold/staffdev/assignments/calcvarb.pdf<http://online.redwoods.cc.ca.us/instruct/darnold/staffdev/assignments/calcvarb.pdf>

Cheers,
Michael



From: getdp [mailto:getdp-bounces at ace20.montefiore.ulg.ac.be] On Behalf Of cristianrivas at aol.com
Sent: Friday, July 25, 2014 9:59 PM
To: getdp at geuz.org
Subject: [Getdp] Question

Dear Sir, I have one question.  On the GetDP webpage the example below (in quotes is provided), but I don't see two derivatives in the Formulation Equation section.  I see { d v } but where is the rest of the div (grad (v)) portion?  Shouldn't there be two derivatives.  Thank you.

Cristian


<Section taken from GetDP website>:
"For example, to solve the Poisson equation div(a grad(v)) = f on a domain D, an input file (".pro" file) would contain something like this:

  FunctionSpace {
    { Name H1; Type Form0;
      BasisFunction {
        { Name sn; NameOfCoef vn; Function BF_Node; Support D; Entity NodesOf[All]; }
      }
    }
  }
  Formulation{
    { Name Poisson; Type FemEquation;
      Quantity {
        { Name v; Type Local; NameOfSpace H1; }
      }
      Equation {
        Galerkin { [ a[] * Dof{d v}, {d v} ] ; In D; Jacobian V; Integration I; }
        Galerkin { [ f[], {v} ] ; In D; Jacobian V; Integration I; }
      }
    }
  } "
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