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Finite Difference - Nonuniform mesh

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Old   April 28, 2009, 07:56
Default Finite Difference - Nonuniform mesh
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I am trying to solve Poissons equation with the use of the finite difference method.

Is there any one that can tell me how the second order derivative lookes like in the interface between a fine and a rough mesh?

I know that this has nothing to do with fluid dynamics, but maybe some one is familiar the finite difference method and is able to help me.

Thanks in advance
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Old   April 28, 2009, 09:21
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You can get the finite difference formula for non uniform mesh by writing the derivative as
f_primeprime = a f_i-1+ b f_i + c f_i-1
Expand the RHS using Taylor's series and match the coefficients on both sides to get a,b anc c.
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Old   May 11, 2009, 18:08
Default finite difference approximation to 2nd derivative
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