Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs
Numerical Analysis
2026-03-24 v1 Numerical Analysis
Abstract
We establish a sparsity in terms of -summability and weighted -summability for the coefficients of the Laguerre generalized piecewise-polynomial chaos expansion of solutions to parametric elliptic PDEs with log-Laplace random inputs. From the sparsity, we derive convergence rates for semi-discrete approximations with respect to parametric variables. These rates are valid for sparse-grid, piecewise-polynomial interpolations and the generated quadratures, and to related extended least-squares approximations and generated quadratures.
Cite
@article{arxiv.2603.21628,
title = {Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs},
author = {Dinh Dũng},
journal= {arXiv preprint arXiv:2603.21628},
year = {2026}
}