An offline-online strategy for multiscale problems with random defects
DOI10.1051/m2an/2022006zbMath1484.65302arXiv2102.01635OpenAlexW4225725077MaRDI QIDQ5061502
Barbara Verfürth, Axel Målqvist
Publication date: 11 March 2022
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.01635
Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) 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) Second-order elliptic equations (35J15) Numerical methods for partial differential equations, boundary value problems (65N99)
Uses Software
Cites Work
- A reduced basis localized orthogonal decomposition
- Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- On multiscale methods in Petrov-Galerkin formulation
- A reduced basis approach for some weakly stochastic multiscale problems
- Efficient implementation of the localized orthogonal decomposition method
- Numerical stochastic homogenization by quasilocal effective diffusion tensors
- Localized orthogonal decomposition for two-scale Helmholtz-type problems
- An Introduction to Computational Stochastic PDEs
- Some variance reduction methods for numerical stochastic homogenization
- A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization
- Localization of elliptic multiscale problems
- Multilevel Monte Carlo Approaches for Numerical Homogenization
- Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions
- Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems
- Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization
- Stochastic finite element methods for partial differential equations with random input data
- Numerical Upscaling of Perturbed Diffusion Problems
- Sparse Compression of Expected Solution Operators
- A Low-Rank Approximated Multiscale Method for Pdes With Random Coefficients
- Numerical Homogenization by Localized Orthogonal Decomposition
- Numerical Homogenization of Elliptic PDEs with Similar Coefficients
- A Control Variate Approach Based on a Defect-Type Theory for Variance Reduction in Stochastic Homogenization
- Quantitative Stochastic Homogenization and Large-Scale Regularity
- Oversampling for the Multiscale Finite Element Method
- Multiscale Finite Element approach for “weakly” random problems and related issues
- A Multilevel Monte Carlo Method for Computing Failure Probabilities
- A Priori Error Analysis of a Numerical Stochastic Homogenization Method
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- A diffuse modeling approach for embedded interfaces in linear elasticity
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