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# Galerkin weighted residuals - tutorial

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I was wondering if there is any kind of tutorial out there, on solving DE using Finite Element Methods, and more exactly, using Galerkin''s Weighted Residuals. First of all, let me clear that this has nothing to do with what you call homework! It has to do with my studies, but it doesn''t related to a specific homework. What i''m searching for, is some examples, on how the method works in 1, 2 and 3 dimensions, with various kinds of basis functions, various BCs (Dirichlet, Neumann). And if possible (and if exists), some examples in code format. I mean, in C/C++ or pseudocode. Please DON''T suggest Fortran code I don''t remember anything from it, and i don''t want to "learn" a language from the beginning!!! I had studied Fortran as a lesson on the 1st semester, but this was 4 years ago (!!!) and i don''t remember anything. I say this, because i have some Fortran code which solves a 2D problem (from one of my teachers), but...! The reason i''m asking for your help on this, is because i want to learn something from it. I don''t want to apply blindly a piece of code, and take some results. Finally i want to say that the above isn''t only terminology. I know what Galerkin''s residuals are, what basis functions are, and how the different kind of BCs affects the solution of the system. What i haven''t seen/learn is how to apply all these to solve a DE. I''ve searched the net, but the only thing i found was theory and only theory. No example! I have a book on the theory, but it has no completed/detailed examples, so i have some "gaps" on my knowledge. Not to mention that the book is very messed up and you can''t follow it easily. Thanks in advance, and i hope someone suggests something. HellRaiZer PS. Also if you have some kind of an introductory book (with examples) to suggest, i''ll try to find it.

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I did a bit of searching:

You might look up that journal issue and examine it, if you havn''t already.
http://www.me.umist.ac.uk/ijmee/28-1.htm

Scanning further, it appears that a numerical anlaysis book with focus on ME topics might contain information.

Heres a help posted for an exam with an example of working Galerkin''s on paper.

http://www.egr.msu.edu/classes/me860/feeny/exams.html

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Thanks for repling!!!

I''ll check those links to see what i can find.

I started working with the general equation (Lu = f) for a 1D problem, on my own, and i have some problems on calculating the integrals that appear in matrix coefs. I think Gauss weighting approximation for solving them will do the trick. I''ll check it too. After that, the only thing that remains is to solve the system. Gauss Elimination is a choice here.

If i finally finish it, and try to write some source on it, i''ll search for more efficient methods.

Thanks once more!!

HellRaiZer

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