deletions | additions       diff --git a/section_Constitutive_relationships_Retardation_factor__.tex b/section_Constitutive_relationships_Retardation_factor__.tex  index 283ddfb..6a325b7 100644  --- a/section_Constitutive_relationships_Retardation_factor__.tex  +++ b/section_Constitutive_relationships_Retardation_factor__.tex 
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Integrate by parts the last term of the left-had side.  \begin{align}  \int_{\Omega} \nabla \cdot \left( D \nabla u \right) s d\Omega = \int_{\Omega} \nabla \cdot  \left( s D \nabla u \right) d\Omega - \int_{\Omega} D \nabla u \nabla s d\Omega \end{align}  Apply Gauss divergence theorem. theorem on the first part of the left-hand side.  \begin{align}  \int_{\Omega} \nabla \cdot \left( s D \nabla u \right) d\Omega = \int_{\Gamma_{N} \cup \Gamma_{D}} s \nabla u \cdot n d\Gamma  \end{align}  Because $s = 0$ on $\Gamma_{D}$.  \begin{align}  \int_{\Omega} \nabla \cdot \left( s D \nabla u \right) d\Omega = \int_{\Gamma_{N}} s \nabla u \cdot n d\Gamma  \end{align}  \begin{align}  \int_{\Omega}\nabla \cdot k \left( h, P \right) \nabla H v\,d\Omega = -\int_{\Omega} k \left( h, P \right) \nabla H \nabla v\,d\Omega + \int_{\Gamma_{N} \cup \Gamma_{D}} k \left( h, P \right) \nabla H v n\,d\Gamma \\  \int_{\Omega}\nabla \cdot k \left( h, P \right) \nabla H v\,d\Omega = -\int_{\Omega} k \left( h, P \right) \nabla H \nabla v\,d\Omega + \int_{\Gamma_{N}} k \left( h, P \right) \nabla H v n\,d\Gamma + \int_{\Gamma_{D}} k \left( h, P \right) \nabla H v n\,d\Gamma  \cdot  \end{align}  Because $v = 0$ on $\Gamma_{D}$.