On 05/14/2017 01:57 AM, hanks0...@gmail.com wrote:
I guess this problem comes from the second derivatives of solution.
I don't know whether the problem really comes from that, but you can't take
the second derivative of a finite element solution without problem. The issue
is that it exists, of course, in the interior of elements. But it is a
delta-function like thing at the interfaces between cells because the finite
element solution is continuous but not continuously differentiable across the
interface (it has a "kink"), and consequently the second derivative consists
of delta functions. I suppose you are not taking them into account in your
formulation.
If you do need second derivatives, you need to either use a C^1 element (quite
difficult to do), or use a mixed formulation in which you rewrite the equation
-Delta q = f into
u + nabla q = 0
-div u = -f
and then use a continuous element for the variable u. This way u=-grad q,
and Delta q = -div u, which you can compute because u is continuous.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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