1 research outputs found
Bilinear quadratures for inner products
A bilinear quadrature numerically evaluates a continuous bilinear map, such
as the inner product, on continuous and belonging to known
finite-dimensional function spaces. Such maps arise in Galerkin methods for
differential and integral equations. The construction of bilinear quadratures
over arbitrary domains in is presented. In one dimension,
integration rules of this type include Gaussian quadrature for polynomials and
the trapezoidal rule for trigonometric polynomials as special cases. A
numerical procedure for constructing bilinear quadratures is developed and
validated