Randomized Projection Operators onto Piecewise Polynomial Spaces
Abstract
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and $H^{-1}$. As smoothers for incomplete or rough data, they yield computable finite element discretizations with optimal convergence rates.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Mathematical Approximation and Integration
Mathematical functions and polynomials
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 4 February 2026
- Document type
- Preprint