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- K. A. Cliffe, Michael B. Giles, Robert Scheichl, Aretha L. Teckentrup
- Computat. and Visualiz. in Science
- 2011

We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method. The main result is that in certain… (More)

- Julia Charrier, Robert Scheichl, Aretha L. Teckentrup
- SIAM J. Numerical Analysis
- 2013

We consider a finite element approximation of elliptic partial differential equations with random coefficients. Such equations arise, for example, in uncertainty quantification in subsurface flow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, have only very… (More)

- Aretha L. Teckentrup, Robert Scheichl, Michael B. Giles, Elisabeth Ullmann
- Numerische Mathematik
- 2013

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and that only have limited spatial regularity. We extend the finite element error analysis for this type of equation, carried… (More)

- A. L. Teckentrup, P. Jantsch, M. Gunzburger, C. G. Webster
- 2014

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic dimension cause an explosion of the computational effort. We propose and analyze a multilevel version of the stochastic… (More)

- Aretha L. Teckentrup
- Proceedings Title: Proceedings of the 2012 Winter…
- 2012

We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random… (More)

Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written… (More)

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior distribution and various approximations based on the Gaussian process emulator. Our analysis includes approximations based on… (More)

In this talk we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo (MCMC) methods for large–scale applications with high dimensional parameter spaces, e.g. uncertainty quantification in porous media flow. We propose a new multilevel Metropolis-Hastings algorithm, and give an abstract, problem dependent… (More)

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