Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors

Michael Barton, Rachid Ait-Haddou, Victor Manuel Calo

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
Original languageEnglish (US)
Pages (from-to)57-70
Number of pages14
JournalJournal of Computational and Applied Mathematics
StatePublished - Mar 21 2017
Externally publishedYes


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