An adaptive variable order quadrature strategy

Houston, Paul; Wihler, Thomas P. (2017). An adaptive variable order quadrature strategy. In: Bittencourt, Marco L.; Dumont, Ney A.; Hesthaven, Jan S. (eds.) Spectral and high order methods for partial differential equations. Lecture Notes in Computational Science and Engineering: Vol. 119 (pp. 533-545). Cham: Springer 10.1007/978-3-319-65870-4_38

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We propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this way we aim to account for local smoothness properties of the integrand as effectively as possible, and thereby achieve highly accurate results in a very efficient manner. Indeed, this idea originates from so-called hp-version finite element methods which are known to deliver high-order convergence rates, even for nonsmooth functions.

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