Department of Computational and Applied Mathematics
We present a simple framework for the construction of bilinear quadratures, which numerically evaluate a continuous bilinear map, such as the L^2 inner product, on continuous f and g belonging to known finite-dimensional function spaces. Such maps commonly arise in Galerkin methods for differential and integral equations. We will discuss the problems of classical quadrature and multivariate interpolation and their close connections to bilinear quadratures. Some numerical examples will be shown.