Generalized  Stokes  equations     Hello,     I   am   interested   to   solve   the   following   set   of   generalized   Stokes   equations   for   the   velocity   v  and  pressure   P :    

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−∇ ⋅ ∇v + ( ∇v ) + ∇P = F

  % ∇P ( −∇ ⋅ v + ∇ ⋅ ' *=0 & Φ )   Here   F  and   are   Φ  prescribed,   nonuniform   vector   and   scalar   fields,   respectively.   The   boundary   of   the   three-­‐dimensional   domain   is   divided   into   two   regions   Γ1  and   Γ 2 .  The  boundary  conditions  on  these  regions  are  as  follows:     Γ1 : v ⋅ n = 0  

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Γ 2 : ∇v + ( ∇v ) ⋅ n − Pn = 0  

  where   n  is  the  unit  vector  outward  normal  to  the  boundary.     Although  this  set  of  differential  equations  is  similar  to  the  one  that  is  solved  in  step-­‐ 22,   it   is   not   clear   to   me   how   (and   whether   it   is   possible)   to   generalize   the   algorithm   of   step-­‐22   to   my   case.   I   would   appreciate   any   advice   regarding   how   to   tackle   this   problem.     Thanks  in  advance,   Oded  Yaakobi