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Laplace Eqn. Finite Diff. Error Problem

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Old   April 4, 2015, 17:33
Default Laplace Eqn. Finite Diff. Error Problem
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Gorkem Ocalan
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I have some problems about error analysis of Laplace Eqn. in 2D. I generated coefficient matrix and right-hand side vector as Au=b format properly and solved u=A\b.

I calculated analytical solution with respect to boundary conditions which are
u(x,0)=0 ,u(x,1)=x-x^2, u(0,y)=0, u(1,y)=0.

There is a problem about error. I was expecting to observe the decrease in error by making the mesh finer. But it did not happen in that way. 41x41 mesh gave better error result than 81x81 mesh.

I also attached the code (MATLAB) for the people who are interested in.

Thanks for your concern...
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File Type: doc problem2.doc (28.0 KB, 4 views)
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Old   April 4, 2015, 17:46
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Filippo Maria Denaro
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indeed, the error must diminuish ... how do you invert A? check if A*A^-1 is the identity matrix (note that u=A^-1*b)
Check also the exact solution
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Old   April 5, 2015, 01:06
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Be careful with MATLAB. Its matrix operations don't always work the way you'd expect.
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