A posteriori error estimations for elliptic partial differential equations with small uncertainties

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The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closed-form or numerical so ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

In this thesis, we conduct a comprehensive investigation into structural instabilities of both elastic and magneto-elastic beams and shells, resulting in a creative proposal to design a programmable braille reader. Methodologically, we combine numerical si ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

Purpose: This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approac ...

In computational hydraulics models, predicting bed topography and bedload transport with sufficient accuracy remains a significant challenge. An accurate assessment of a river's sediment transport rate necessitates a prior understanding of its bed topograp ...

As a follow-up to the CEA-EPFL PETALE experimental program on stainless steel nuclear data, the EPFL initiated an open-loop pile-oscillation experimental program in the CROCUS reactor: BLOOM. A reproduction of the critical experiments of PETALE, the progra ...

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Chattez avec Graph Search

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Stability: a search for structure

From low-rank retractions to dynamical low-rank approximation and back

Spectral Estimators for High-Dimensional Matrix Inference

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

The time-domain Cartesian multipole expansion of electromagnetic fields

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Reliable data-driven decision-making through optimal transport

Instabilities in Elastic and Magneto-Elastic Beams and Shells: from Shell Buckling to the Design of a Programmable Braille Reader

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

Stochastic Simulations and Machine Learning Modeling to Predict Bedload Transport and Bed Topography

Design of an Open-Loop Pile-Oscillation Program in the CROCUS Reactor