Finite element method: Difference between revisions

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\textrm{(*) }\ \ \ \forall e_j \in \mathrm{E} : \psi\left(u,e_j\right)=\int_T g\cdot e_j.
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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>
(**) &psi;(''u<sub>n</sub>'',''e<sub>j</sub>'')=&int;<sub>T</sub>''g'' &middot; ''e'<sub>j</sub>'' for every ''e<sub>j</sub>'' in F<sub>''n''</sub>
\textrm{(**)}\ \ \forall e_j \in \mathrm{F}_n : \psi\left(u_n,e_j\right)=\int_T g\cdot e_j
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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 (*)