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

An Adaptive Multiscale Finite Element Method

This work is devoted to an adaptive multiscale finite element method (MsFEM) for solving elliptic problems with rapidly oscillating coefficients. Starting from a general version of the MsFEM with oversampling, we derive an a posteriori estimate for the H-1 ...

Siam Publications2014

MATHICSE Technical Report : 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 ...

MATHICSE2014

Liouville's theorem and Laurent Series Expansions for Solutions of the Heat Equation

Aparajita Dasgupta

We give a Liouville theorem for entire solutions and Laurent series expansions for solutions with isolated singularities of the heat equation. ...

Springer Basel Ag2014

Shortest-Weight Paths In Random Regular Graphs

Léo Hamed Amini

Consider a random regular graph with degree d and of size n. Assign to each edge an independent and identically distributed exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edge ...

Siam Publications2014

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

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

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan

The identification of kinetic models is an important step for the monitoring, control and optimization of industrial processes. This is particularly the case for highly competitive business sectors such as chemical and pharmaceutical industries, where the ...

2013

MATHICSE Technical Report : 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 ...

MATHICSE2013

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan, Benoit Till Cretegny

Identification of kinetic models and estimation of reaction and mass-transfer parameters can be performed using the extent-based identification method, whereby each chemical/physical process is handled separately [1-3]. This method is used here to analyze ...

2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method

Assyr Abdulle, Achim Nonnenmacher

We present an "a posteriori" error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro-to-micro formulation, where the macrosco ...

Wiley-Blackwell2013

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

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An Adaptive Multiscale Finite Element Method

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Liouville's theorem and Laurent Series Expansions for Solutions of the Heat Equation

Shortest-Weight Paths In Random Regular Graphs

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Shortest-Weight Paths In Random Regular Graphs

An Adaptive Multiscale Finite Element Method

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Liouville's theorem and Laurent Series Expansions for Solutions of the Heat Equation

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method