Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data
DOI10.1137/15M1044266zbMath1355.60091arXiv1510.02708MaRDI QIDQ2953223
Mattias Sandberg, Raúl Tempone, Anders Szepessy, Eric J. Hall, Håkon Hoel
Publication date: 4 January 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1510.02708
Monte Carlo methodselliptic PDEa posteriori errorquadrature errorrandom PDEGalerkin errorrough stochastic data
Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)
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- Multi-index Monte Carlo: when sparsity meets sampling
- 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 stochastic Galerkin FEM
- Mixed finite element analysis of lognormal diffusion and multilevel Monte Carlo methods
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
- A posteriori error estimation in finite element analysis
- Finite elements for elliptic problems with stochastic coefficients
- On solving elliptic stochastic partial differential equations
- A continuation multilevel Monte Carlo algorithm
- Convergence rates for an adaptive dual weighted residual finite element algorithm
- Stochastic simulation: Algorithms and analysis
- An adaptive stochastic Galerkin method for random elliptic operators
- Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo
- Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods
- Multilevel Monte Carlo Path Simulation
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
- Error Estimates for Adaptive Finite Element Computations
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- Adaptive weak approximation of stochastic differential equations
- Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
- STOCHASTIC GALERKIN DISCRETIZATION OF THE LOG-NORMAL ISOTROPIC DIFFUSION PROBLEM
- The Mathematical Theory of Finite Element Methods
- The Rate of Convergence for the Finite Element Method
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- Solution of stochastic partial differential equations using Galerkin finite element techniques