Publications related to A posteriori error estimation for partial differential equations with random input data

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

In this work we discuss the dynamically orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

2015

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

MATHICSE Technical Report : Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems

Andrea Manzoni, Nicola Parolini

We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...

MATHICSE2015

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion ...

Univ Washington, Dept Mathematics2015

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

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The CMLMC algorithm so ...

MATHICSE2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. Moreover, we discuss extensions to non-unif ...

MATHICSE2014

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Fabio Nobile, Eleonora Musharbash

In this work we discuss the Dynamically Orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

MATHICSE2014

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number

N

of random inputs and an analytic dependence of the s ...

2014

A posteriori error estimation for partial differential equations with random input data

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Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

MATHICSE Technical Report : Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems

Lyapunov exponents of random walks in small random potential: the upper bound

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

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Perturbation analysis for the Darcy problem with log-normal permeability

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

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Lyapunov exponents of random walks in small random potential: the upper bound

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

MATHICSE Technical Report : Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs