# how to caculate the Galerkin projection

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 March 15, 2006, 08:46 how to caculate the Galerkin projection #1 ztdep Guest   Posts: n/a hell0: I don not how to caculate the Galerkin projection. ( laplace(T), phi ) Where phi is the basis, and i want to project the laplace(T) onto the phi, but 1), what is the meaning of ( ) , and i have the value of T only at discrete points, then how to caculate it. regards!

 March 15, 2006, 09:34 Re: how to caculate the Galerkin projection #2 al Guest   Posts: n/a Let us assume a(x) and b(x) two functions in an interval [0,1]. Then (a,b)=integral a(x) b(x) dx means the inner product, (dot product), between the functions a and b. This can be considered as a projection of a() into b() and the other way around. This is much more simple, for the case of simple vectors, e.g. a=[1 0 1] and b=[1 0 0] (a,b) = |a| |b| cos( angle (a,b) ) Equivalent, (laplace(T),phi) means that you want to determine the projection of laplace(T) into phi. Why do you have only discrete points? Are you using a Galerkin spectral method? Any way, if you have only T at some points, e.g. T[i] , then you can compute approximately laplace(T) at the same points, laplace(T)[i]. Then you can approximate the inner product as (laplace(T),phi)= laplace(T)[1] phi[1] Deltax + laplace(T)[2] phi[2] Deltax+ ... where Deltax is the space between the points.

 March 15, 2006, 21:36 Re: how to caculate the Galerkin projection #3 ztdep Guest   Posts: n/a Hi,Wed: thank you for your feedback! would you like to give me your email address, i have some question! regards!

 March 15, 2006, 23:52 Re: how to caculate the Galerkin projection #4 Mike Guest   Posts: n/a

 March 16, 2006, 01:03 Re: how to caculate the Galerkin projection #5 ztdep Guest   Posts: n/a Mike: what have you give me! i can not get any information from it? then how to use it

 March 16, 2006, 01:49 Re: how to caculate the Galerkin projection #6 Mike Guest   Posts: n/a My name is "Michail" and I'm Russian in Russian it means "BEAR" http://community.livejournal.com/ru_preved/ Bear is our natianal HERO

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