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Fininte difference and Finite element Technique

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Old   December 21, 2005, 00:41
Default Fininte difference and Finite element Technique
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Mahendra Singh Mehra
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my question is

what is the difference in finite difference method and finite element method and why Fininte difference is used for Fluid analysis and Finite element for solid mechanics.

is there any difference in solving techniques these two methods.

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Mehra
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Old   December 22, 2005, 02:05
Default Re: Fininte difference and Finite element Techniqu
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sumedh
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Following excerpt from Vivek Ranade's book will answer your question to some extent. "The distinguishing feature of FE method is that the equation are multiplied by weight function before they are integrated over the entire domain. This approximation is then substituted into the weighted integral of the conservation law. By minimizing the residual, a set of non-linear algebraic equations is obtained. An important advantage of the FE method is its superior ability to deal with a solution domain having complex geometry, It is however difficult to develop computationally efficient solution method for strongly coupled and non-linear equations using FE."

Sumedh

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Old   December 22, 2005, 10:08
Default Re: Fininte difference and Finite element Techniqu
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Mahendra Singh Mehra
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Sumedh,

Thanks for your prompt reply and giving insight of FE method. but FD method is still unanswered.

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Mehra
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Old   December 23, 2005, 00:49
Default Re: Fininte difference and Finite element Techniqu
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sumedh
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Again the excerpt from the same book. " The finite volume (FV) method uses the intergal form of the conservation equation as its starting point. The solution domain is divided into number of computational cells. The differential equation is integrated over the volume of each computational cell to obtain the algebraic equation". Those equations are solved iteratively to get the solution over the entire domain. Even if you start with FV method than also you will get the same form of algebraic equations as with FD method. For most of the cases FV and FD method and FD method is same, only approach is differetnt.

Sumedh
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