Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities
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Publication:4571042
DOI10.1137/16M1104986zbMath1397.65275arXiv1611.06012OpenAlexW2964025847MaRDI QIDQ4571042
Ralf Kornhuber, Evgenia Youett
Publication date: 6 July 2018
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1611.06012
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Monte Carlo methods (65C05) 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)
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Cites Work
- Unnamed Item
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- Axioms of adaptivity
- 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
- Adaptive numerical solution of PDEs.
- Optimization of mesh hierarchies in multilevel Monte Carlo samplers
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- A multilevel iterative method for symmetric, positive definite linear complementarity problems
- The DUNE-subgrid module and some applications
- Monotone multigrid methods for elliptic variational inequalities. I
- Adaptive finite element methods with convergence rates
- Multilevel Monte Carlo method for parabolic stochastic partial differential equations
- Simplicial grid refinement: On Freudenthal's algorithm and the optimal number of congruence classes
- A continuation multilevel Monte Carlo algorithm
- Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems
- Decay rates of adaptive finite elements with Dörfler marking
- Hierarchical error estimates for the energy functional in obstacle problems
- Convergence analysis of a conforming adaptive finite element method for an obstacle problem
- Optimality of a standard adaptive finite element method
- Adaptive Multilevel Monte Carlo Simulation
- Multilevel Monte Carlo Methods
- An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data
- Multilevel Monte Carlo Path Simulation
- Concepts of an adaptive hierarchical finite element code
- Adaptive multivlevel methods in three space dimensions
- A class of random variational inequalities and simple random unilateral boundary value problems - existence, discretization, finite element approximation
- Continuous Level Monte Carlo and Sample-Adaptive Model Hierarchies
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- A Convergent Adaptive Algorithm for Poisson’s Equation
- A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions
- Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
- Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities
- Global convergence rate of a standard multigrid method for variational inequalities
- Implementation and analysis of an adaptive multilevel Monte Carlo algorithm
- Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs
- A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements
- On a Class of Random Variational Inequalities on Random Sets
- A Multilevel Monte Carlo Method for Computing Failure Probabilities
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
