Title: Old and new uses of Garding-type inequalities in numerical analysis of the Helmholtz equation.
Abstract: The concept of a Garding inequality is key in the analysis of second-order linear elliptic PDEs such as the Helmholtz equation. This concept is also key in the numerical analysis of the finite-element method (FEM) -- a very popular method for computing approximations to solutions of the Helmholtz equation.
In this talk I will review the classic uses of the Garding inequality in the FEM for Helmholtz, and then present a new use of a Garding-type inequality in this context.
No knowledge of numerical analysis or the finite-element method will be needed to understand this talk!