Laplace Eqn. Finite Diff. Error Problem

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April 4, 2015, 17:33
Laplace Eqn. Finite Diff. Error Problem
#1
New Member

Gorkem Ocalan
Join Date: Feb 2015
Posts: 5
Rep Power: 4
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...
Attached Files
 problem2.doc (28.0 KB, 4 views)

 April 4, 2015, 17:46 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,409 Rep Power: 39 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

 April 5, 2015, 01:06 #3 Member   Alex Join Date: Jan 2014 Posts: 54 Rep Power: 5 Be careful with MATLAB. Its matrix operations don't always work the way you'd expect.

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