|April 4, 2015, 17:33||
Laplace Eqn. Finite Diff. Error Problem
Join Date: Feb 2015
Posts: 5Rep Power: 4
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...
|April 4, 2015, 17:46||
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,993Rep Power: 34
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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