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<math>
\textrm{(*)
</math>
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In order to turn this process into an algorithm that can be run on actual hardware, one chooses a finite subset of E. Now we have F=F<sub>''n''</sub>={e<sub>1</sub>,e<sub>2</sub>,...,e<sub>n</sub>} a finite set, F a subset of E, and we wish to solve the problem
<math>
\textrm{(**)}\ \ \forall e_j \in \mathrm{F}_n : \psi\left(u_n,e_j\right)=\int_T g\cdot e_j
</math>
with the goal that, as ''n'' increases to infinity (and F<sub>''n''</sub> increases to E), the solutions ''u<sub>n</sub>'' should converge to the solution ''u'' of (*)
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