An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data

DOI10.1137/15M1016448zbMath1398.35306MaRDI QIDQ3179327

Johannes Neumann, C. Merdon, Martin Eigel

Publication date: 21 December 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

zbMATH Keywords

adaptive methodsuncertainty quantificationmultilevel Monte Carlopartial differential equations with random coefficients

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with randomness, stochastic partial differential equations (35R60) Random linear operators (47B80) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items (19)

Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation ⋮ A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data ⋮ An adaptive hp-version stochastic Galerkin method for constrained optimal control problem governed by random reaction diffusion equations ⋮ Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients ⋮ Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities ⋮ Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs ⋮ Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates ⋮ Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification ⋮ Goal-oriented adaptive modeling of random heterogeneous media and model-based multilevel Monte Carlo methods ⋮ Continuous Level Monte Carlo and Sample-Adaptive Model Hierarchies ⋮ $hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Navier--Stokes Equations ⋮ Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs ⋮ Quantifying discretization errors for soft tissue simulation in computer assisted surgery: a preliminary study ⋮ An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system ⋮ Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations ⋮ Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification ⋮ Multifidelity Monte Carlo Estimation with Adaptive Low-Fidelity Models ⋮ Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method ⋮ Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

Uses Software

• ALEA
• DFVLR-SQP

Cites Work

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