My FEM scheme uses a 4-node quadrilateral element with bilinear shape functions. The simple problem I'm solving is. $\nabla ^2 f = 5$ But as I increase the number of nodes, the plot of the solution becomes flatter. I'm stumped as to why this might happen.Two plots below show how when I change the size of the mesh from a 7x7 to a approx. 30x30, the plot becomes much more spread out. Also the boundary condition is that $f = 0$ on the boundary

7x7 mesh

30x30 mesh

FIXED, had some typos in my code

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    $\begingroup$ The result is obviously wrong. I think there is a mistake in your code but it's impossible to say what the mistake is without seeing the code. $\endgroup$ – knl Sep 22 '20 at 4:52
  • $\begingroup$ The fact that the solution changes significantly when you refine your grid hints in the direction, that some h-dependent scaling might have been forgotten. Can you give us a bit more information? What code are you using, do you have a minimal working example? Do you have a 1D example that you might check first? $\endgroup$ – MPIchael Sep 24 '20 at 13:42

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