Applied Mathematics Colloquium

  The Galerkin and Petrov-Galerkin methods provide an abstract, functional-analytic foundation for the analysis of the finite element method in numerical PDEs. In this talk, I will introduce these methods and some of the classical estimates, which can be described with few analytical prerequisites beyond the theory of Hilbert and Banach spaces. I will then discuss some recent work showing that one of these classical error estimates, due to Babuska (1971), can be sharpened by considering the relationship between Banach space geometry and projection operators.