Stable High Order Quadrature Rules for Scattered Data and General Weight Functions

Abstract

Numerical integration is encountered in all fields of numerical analysis and the engineering sciences. By now, various efficient and accurate quadrature rules are known; for instance, Gauss-type quadrature rules. In many applications, however, it might be impractical---if not even impossible---to obtain data to fit known quadrature rules. Often, experimental measurements are performed at equidistant or even scattered points in space or time. In this work, we propose stable high order quadrature rules for experimental data, which can accurately handle general weight functions.

arXiv commentAccepted at SINUM

References in corpus (1)

• Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points

Cited by in corpus (8)

• Stable high-order cubature formulas for experimental data
• Summation-by-parts operators for general function spaces
• Construction and application of provable positive and exact cubature formulas
• Towards Stable Radial Basis Function Methods for Linear Advection Problems
• Stabilizing Radial Basis Function Methods for Conservation Laws Using Weakly Enforced Boundary Conditions
• Towards stability of radial basis function based cubature formulas
• Towards stability results for global radial basis function based quadrature formulas
• Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction