The paper provides sufficient conditions on parametric regularity for QMC error bounds in finite element discretizations of parametric PDEs with Gevrey-regular random fields, achieving faster-than-MC rates when the quantity of interest depends continuously on the solution, flux, or gradient.
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Numerical tests indicate that a stochastic Galerkin discretization with embedded slabwise space-time finite elements and GMRES-GMG solvers outperforms Monte-Carlo sampling for random parabolic problems in convergence and algebraic solver statistics.
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Sufficient conditions for QMC analysis of finite elements for parametric differential equations
The paper provides sufficient conditions on parametric regularity for QMC error bounds in finite element discretizations of parametric PDEs with Gevrey-regular random fields, achieving faster-than-MC rates when the quantity of interest depends continuously on the solution, flux, or gradient.
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Stochastic Galerkin and Monte-Carlo methods for parabolic problems: Numerical performance of variational matrix-free approximations
Numerical tests indicate that a stochastic Galerkin discretization with embedded slabwise space-time finite elements and GMRES-GMG solvers outperforms Monte-Carlo sampling for random parabolic problems in convergence and algebraic solver statistics.