Finite element method: Difference between revisions

Revision as of 09:25, 27 January 2004

Revision as of 13:09, 27 January 2004

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We denote by V^* the set of all such functionals. Then, certainly, the following statements are equivalent:

:<math>

: L''u''=''g''

\mathrm{L}u=g

</math>

and

:<math>

: For all &phi; in V^*, &phi;(L''u'')=&phi;(''g'')

\forall \phi \in \mathrm{V}^*: \phi\left(\mathrm{L}u\right)=\phi\left(g\right).

</math>

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