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April 4, 2015, 17:33 |
Laplace Eqn. Finite Diff. Error Problem
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#1 |
New Member
Gorkem Ocalan
Join Date: Feb 2015
Posts: 5
Rep Power: 11 |
Hi,
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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April 4, 2015, 17:46 |
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#2 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,764
Rep Power: 71 |
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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April 5, 2015, 01:06 |
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#3 |
Member
Alex
Join Date: Jan 2014
Posts: 54
Rep Power: 12 |
Be careful with MATLAB. Its matrix operations don't always work the way you'd expect.
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