Auth: Martin J. Gander (in collaboration with Gerhard Wanner)
Book Summary: This text offers a comprehensive historical and mathematical review tracing the evolution of numerical methods that eventually led to the modern Finite Element Method (FEM). Instead of presenting FEM purely as a modern computational tool, this work maps out the progressive intellectual milestones established by foundational mathematicians and engineers.
The paper covers the early calculus of variations foundations laid by Euler and Lagrange, Walther Ritz’s pioneering work using global trial functions to solve boundary value problems, and Boris Galerkin’s crucial modification using weighted residuals. Finally, it highlights Richard Courant’s definitive contribution—introducing localized, piecewise linear trial functions over triangular subdomains—which effectively bridged the gap between classical variational mathematics and modern finite element analysis. It is an excellent read for researchers seeking a deep historical perspective on the mathematical foundations of computational mechanics.
