= Richard Courant
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<Richard Courant> connected mathematical analysis with practical methods for <partial differential equations>. His 1943 paper develops <variational methods> for equilibrium and vibration problems, including finite-parameter approximations.<Variational methods for the solution of problems of equilibrium and vibrations by Richard Courant>[Original paper, variational approximation and piecewise-linear constructions]{ref}
A trial solution can be built from <piecewise linear functions> on a <triangulation>. Minimizing the energy over their coefficients replaces an infinite-dimensional problem with a finite <linear system>. This construction became part of the foundations of the <finite element method>, showing how geometric subdivision and a variational principle can work together. The approach combines variational ideas with local geometric approximation.
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