Repository: Freie Universit├Ąt Berlin, Math Department

Quasi-Monte Carlo and discontinuous Galerkin

Kaarnioja, Vesa and Rupp, Andreas (2024) Quasi-Monte Carlo and discontinuous Galerkin. arXiv . (Submitted)

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Official URL: https://doi.org/10.48550/arXiv.2207.07698

Abstract

In this study, we consider the development of tailored quasi-Monte Carlo (QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial differential equations (PDEs) with random coefficients. We consider both the affine and uniform and the lognormal models for the input random field, and investigate the use of QMC cubatures to approximate the expected value of the PDE response subject to input uncertainty. In particular, we prove that the resulting QMC convergence rate for DG approximations behaves in the same way as if continuous finite elements were chosen. Notably, the parametric regularity bounds for DG, which are developed in this work, are also useful for other methods such as sparse grids. Numerical results underline our analytical findings.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3106
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 15:40
Last Modified:19 Feb 2024 15:40

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