Finite element method: Difference between revisions

Revision as of 13:12, 27 January 2004

Revision as of 13:15, 27 January 2004

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The latter statement is said to be the ''weak form'' of our problem. One can think of it as emphasizing that the simple equality

:<math>

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

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

</math>

for a single &phi; in V^* is insufficient to imply L''u'' = ''g'', and thus it is weaker. The true meaning of the nomenclature is related to the so-called weak [[topology]] for Banach spaces, which is induced by V^*, but this is beyond the scope of this article.

=== The bilinear form of L, test functions ===