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## Re: [Libmesh-users] Non-homogeneous Neumann Boundary Condition

 Re: [Libmesh-users] Non-homogeneous Neumann Boundary Condition From: John Peterson - 2009-09-02 20:23:03 ```On Wed, Sep 2, 2009 at 2:38 PM, Vijay S. Mahadevan wrote: > On first look, I would say that the neumann_value is supposed to be > -0.25 and not -0.5 at x=2. Try this change and see if it resolves the > bug. Also like John suggested, see if your L2 and H1 errors give right > convergence orders. I don't see anything obviously wrong... If the original problem is: d/dx (x * du/dx) = 2/x^2 The weak form is: -(x u',v') + x u'(2) v(2) - x u'(1) v(1) = (2/x^2,v) Bringing the right endpoint bc over to the rhs and assuming the Dirichlet bc is handled, -(x u',v') = (2/x^2,v) - x u'(2) v(2) And replacing with the Neumann condition, (-x * du/dx) = 0.5 @ x = 2, we get -(x u',v') = (2/x^2,v) + 0.5 v(2) Multiplying thru by neg. 1 as in the code, we get (x u',v') = -(2/x^2,v) - 0.5 v(2) If the theoretical convergence rates are off, I would probably start by looking at the endpoint integral, though there may be something else obvious I'm missing. -- John ```