Randomized Projection Operators onto Piecewise Polynomial Spaces

2026/02/28 by Johannes Storn
Computer Science · Mathematics · #cs.NA #math.NA #msc:65D30 #msc:65D32 #msc:65N15 #msc:65N30 #msc:65N50

paper · pdf · doi:10.48550/arxiv.2602.04490

arxiv created 2026/08/06 · arxiv updated 2026/08/07

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 L² and H^-1. As smoothers for incomplete or rough data, they yield computable finite element discretizations with optimal convergence rates.

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