2022/07/15 by Vesa Kaarnioja, Kaarnioja, Vesa, Andreas Rupp +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2207.07698
openalex publication_date 2022/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.