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MATHICSE Technical Report : A probabilistic finite element method based on random meshes: Error estimators and Bayesian inverse problems

Related publications (40)

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Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...

Springer Heidelberg2016

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This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the ...

MATHICSE2015

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...

MATHICSE2014

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

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We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...

Elsevier2013

On the Automatic Computation of Error Bounds for Solutions of Nonlinear Equations

Viktor Kuncak, Eva Darulova

A large portion of software is used for numerical calculations in mathematics, physics and engineering applications. Among the things that make verification in this domain difficult is the quantification of numerical errors, such as roundoff errors and err ...

2012

Certifying Solutions for Numerical Constraints

Viktor Kuncak, Eva Darulova

A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...

2012

Adaptive Finite Element Methods for Multiscale Partial Differential Equations

Achim Nonnenmacher

Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...

EPFL2011

Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In ou ...

2011

MAV-based real-time localisation of terrestrial targets with cm-level accuracy: Feasibility study

Jan Skaloud, Yosef Akhtman, Abhinav Garg

We carry out a comprehensive feasibility study for a real-time cm-level localisation of a predefined terrestrial target from a MAV-based autonomous platform. Specifically, we conduct an error propagation analysis which quantifies all potential error source ...

2011