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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi Cristian,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">the PDEs for GetDP have to be in weak form (</span><span lang="EN-US" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:black">see
</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><a href="http://en.wikipedia.org/wiki/Weak_formulation">http://en.wikipedia.org/wiki/Weak_formulation</a>).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The equation you mentioned (</span><code><span lang="EN-US" style="font-size:11.5pt;color:#252525">div(a grad(v)) = f)
</span></code><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">is in strong form and has to be<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">converted to the weak form before being implemented in GetDP. For more on this topic
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">please have a look at one of the books mentioned in the wiki (<a href="https://geuz.org/trac/getdp/wiki/TheoreticalReferences">https://geuz.org/trac/getdp/wiki/TheoreticalReferences</a>):<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Understanding and Implementing the Finite Element Method - Mark S. Gockenbach - ISBN 978-0-898716-14-6<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Numerical Methods in Scientific Computing - J. van Kan, A. Segal, F. Vermolen - ISBN 90-71301-50-8 -
</span><a href="http://www.vssd.nl/hlf/a002.htm"><span class="icon"><span lang="EN-US" style="color:blue"></span></span><span lang="EN-US">http://www.vssd.nl/hlf/a002.htm</span></a><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">Introduction to the Calculus of Variations - Jim Fischer:
</span><a href="http://online.redwoods.cc.ca.us/instruct/darnold/staffdev/assignments/calcvarb.pdf"><span class="icon"><span lang="EN-US" style="color:blue"></span></span><span lang="EN-US">http://online.redwoods.cc.ca.us/instruct/darnold/staffdev/assignments/calcvarb.pdf</span></a><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">Cheers</span>,<o:p></o:p></p>
<p class="MsoNormal">Michael<o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> getdp [mailto:getdp-bounces@ace20.montefiore.ulg.ac.be]
<b>On Behalf Of </b>cristianrivas@aol.com<br>
<b>Sent:</b> Friday, July 25, 2014 9:59 PM<br>
<b>To:</b> getdp@geuz.org<br>
<b>Subject:</b> [Getdp] Question<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:black">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.<br>
<br>
Cristian<br>
<br>
<br>
<Section taken from GetDP website>:<br>
"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:<br>
<br>
FunctionSpace {<br>
{ Name H1; Type Form0; <br>
BasisFunction {<br>
{ Name sn; NameOfCoef vn; Function BF_Node; Support D; Entity NodesOf[All]; }<br>
}<br>
}<br>
}<br>
Formulation{<br>
{ Name Poisson; Type FemEquation;<br>
Quantity { <br>
{ Name v; Type Local; NameOfSpace H1; }<br>
}<br>
Equation {<br>
Galerkin { [ a[] * Dof{d v}, {d v} ] ; In D; Jacobian V; Integration I; }<br>
Galerkin { [ f[], {v} ] ; In D; Jacobian V; Integration I; }<br>
}<br>
}<br>
} "</span><o:p></o:p></p>
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