On the robustness of variational multiscale error estimators for the forward propagation of uncertainty

DOI10.1016/j.cma.2018.07.041zbMath1440.65196OpenAlexW2887037249WikidataQ129394182 ScholiaQ129394182MaRDI QIDQ1986396

Oriol Colomés, Guglielmo Scovazzi, Johann Guilleminot

Publication date: 8 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2018.07.041

zbMATH Keywords

variational multiscale methoda posteriori error estimationuncertainty propagationconvection-diffusion-reaction equation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (3)

Anisotropic VMS solution of advection-diffusion problems by spectral approximation of sub-grid scales ⋮ A review of VMS a posteriori error estimation with emphasis in fluid mechanics ⋮ A posteriori error estimation and adaptivity based on VMS for the incompressible Navier-Stokes equations

Uses Software

• FEMPAR

Cites Work

• A Mathematical Theory of Communication
• A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies
• Uncertainty propagation using Wiener-Haar expansions
• Sparse pseudospectral approximation method
• The variational multiscale method -- a paradigm for computational mechanics
• On stabilized finite element methods for linear systems of convection-diffusion-reaction equations
• A numerical study of a posteriori error estimators for convection-diffusion equations
• A simple subgrid scale stabilized method for the advection-diffusion-reaction equation
• Variational multiscale a posteriori error estimation for systems: the Euler and Navier-Stokes equations
• Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty
• Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows
• Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
• On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
• A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method
• Output-based error estimation and mesh adaptation for variational multiscale methods
• Variational multiscale error estimators for solid mechanics adaptive simulations: an orthogonal subgrid scale approach
• The multiscale approach to error estimation and adaptivity
• Proper intrinsic scales for a posteriori multiscale error estimation
• Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Variational multiscale a posteriori error estimation for multi-dimensional transport problems
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Assessment measures for URANS/DES/LES: an overview with applications
• Handbook of Uncertainty Quantification
• Reduced chaos expansions with random coefficientsin reduced-dimensional stochastic modeling of coupled problems
• Information Theory and Statistical Mechanics
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• Spectral Methods for Uncertainty Quantification
• A‐posteriori error estimates for the finite element method
• Turbulent Flows
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Variational Multiscale Analysis: the Fine‐scale Green’s Function, Projection, Optimization, Localization, and Stabilized Methods
• Robust a-posteriori estimator for advection-diffusion-reaction problems

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