PreprintCC BY 4.0arXiv
A General Superconvergence Result for Cubature on Tesselated Polytopal Domains in Two and Three Dimensions
Abstract
Cubature rules, which approximate definite integrals as a linear combination of a set of function values, are ubiquitous and necessary for computational methods in the physical sciences. A superconvergence result for cubature rules on polytopal domains in two and three dimensions is developed, whereby a rule that is exact for all bivariate polynomials of a fixed even degree realizes an extra order of convergence under a decrease in the spacing between nodes.
Related
- Scaled boundary cubature scheme in higher dimensions: integration over polytopes and curved regions
- Superconvergence of Centered Finite Difference Approximations
- An Implementation-Friendly SDG Scheme based on Cartesian Grids for Stokes Equations with Pressure Robustness and Superconvergence
- Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes
- Parametric Families of Minimal Positive Cubature Formulas of Degrees 4 and 6 on the 2-Sphere
BibTeX
@misc{reeger2026general,
title = {{A General Superconvergence Result for Cubature on Tesselated Polytopal Domains in Two and Three Dimensions}},
author = {Jonah A. Reeger},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28883},
eprint = {2608.28883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A General Superconvergence Result for Cubature on Tesselated Polytopal Domains in Two and Three Dimensions
AU - Jonah A. Reeger
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.28883
UR - https://arxiv.org/abs/2608.28883
AB - Cubature rules, which approximate definite integrals as a linear combination of a set of function values, are ubiquitous and necessary for computational methods in the physical sciences. A superconvergence result for cubature rules on polytopal domains in two and three dimensions is developed, whereby a rule that is exact for all bivariate polynomials of a fixed even degree realizes an extra order of convergence under a decrease in the spacing between nodes.
ER -