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arXiv · 2603.21628

Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs

Dinh Dũng
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Abstract

We establish a sparsity in terms of $\ell_p$-summability and weighted $\ell_2$-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.

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Dinh Dũng. 2026-03-23. Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs. https://arxiv.org/abs/2603.21628

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