Quadrature blending for isogeometric analysis

We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. To explain the observed behavior and quantify the approximation errors, we use the generalized Pythagorean eigenvalue error theorem to account for quadrature errors on the resulting weak forms [28]. The proposed blended techniques improve the spectral accuracy of isogeometric analysis on uniform and non-uniform meshes for different polynomial orders and continuity of the basis functions. The convergence rate of the optimally blended schemes is increased by two orders with respect to the case when standard quadratures are applied. Our technique can be applied to arbitrary high-order isogeometric elements.