25 Sep 2015  ·  Wong Christopher A. ·

A bilinear quadrature numerically evaluates 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 arise in Galerkin methods for differential and integral equations... The construction of bilinear quadratures over arbitrary domains in \$\mathbb{R}^d\$ 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. read more

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