Parametric Regularity Analysis and Quasi-Monte Carlo Cubature for Discontinuous Galerkin Approximations of Elliptic PDEs with Random Coefficients

The core message of this paper is to develop a tailored quasi-Monte Carlo (QMC) cubature framework for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial differential equations with random coefficients. The authors prove that the resulting QMC convergence rate for DG approximations behaves in the same way as if continuous finite elements were chosen, and provide a detailed parametric regularity analysis for DG solutions.