On product integration rules for highly oscillatory integrals on a triangle

In this paper, we are concerned with a product rule on triangle. After introducing a natural grid configuration, a Lagrange interpolation polynomial of total degree is given explicitly and proved to be unisolvent. The corresponding error expression is also given. Moreover, with the unisolvence of the multivariate interpolation, the Filon method can be constructed provided by the exact moment computation. Adding more inner nodes contributes to improve the accuracy for the whole regime of the oscillatory parameter. Numerical experiments are provided to illustrate the effectiveness of the proposed method.(c) 2022 Elsevier B.V. All rights reserved.