Adaptive Quasi-Monte Carlo Finite Element Methods for Parametric Elliptic PDEs

Abstract We introduce novel adaptive methods to approximate moments of solutions partial differential Equations (PDEs) with uncertain parametric inputs. A typical problem in Uncertainty Quantification is the approximation expected values quantities interest solution, which requires efficient numerical high-dimensional integrals. perform this task by a class deterministic quasi-Monte Carlo integration rules derived from Polynomial lattices, that allows control a-posteriori error without querying governing PDE and does not incur curse dimensionality. Based on an abstract formulation finite element (AFEM) for problems, we infer convergence combined algorithms parameter physical space. propose selection examples PDEs admissible these algorithms. Finally, present evidence model diffusion PDE.