English

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 p\ell_p-summability and weighted 2\ell_2-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.

Keywords

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}
}
R2 v1 2026-07-01T11:32:48.432Z