Finite element method: Difference between revisions

Revision as of 13:29, 27 January 2004

Revision as of 17:24, 27 January 2004

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The set V^* is larger than it absolutely needs to be. It turns out that it suffices to use functionals of the form

:<math>

:&phi;_''v''(f)=&int;₀¹&int;₀¹''v''(x,y)''f''(x,y)dxdy,

\phi_v\left(f\right)=\int_0^1\int_0^1 v\left(x,y\right) f\left(x,y\right) dxdy,

</math>

where ''v'' satifies the specified (periodic) boundary conditions.

That is, we are now replacing the original problem with that of finding ''u'' in V so that

:<math>

\phi_v\left(\mathrm{L}u\right)=\phi_v\left(g\right)

</math>

:&phi;_''v''(L''u'')=&phi;_''v''(''g'')