Publications related to A posteriori error estimation for the steady Navier-Stokes equations in random domains

Spectral Estimators for High-Dimensional Matrix Inference

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 ...

EPFL2024

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Marco Picasso, Paride Passelli

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 ...

Walter De Gruyter Gmbh2024

An equilibrated flux a posteriori error estimator for defeaturing problems

Annalisa Buffa, Denise Grappein, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

2023

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes that are unfitted with the described physical object. T ...

2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

Assyr Abdulle, Giacomo Garegnani

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...

ELSEVIER SCIENCE SA2021

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Nonlinear Finite Elements in Dynamics

This report focuses on the implementation of the finite element method for nonlinear dynamical problems arising in solid mechanics. The theory of continuum mechanics is extensively covered in the literature and it is assumed the reader is already familiar ...

2020

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

A posteriori error estimation for the steady Navier-Stokes equations in random domains

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Spectral Estimators for High-Dimensional Matrix Inference

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

An equilibrated flux a posteriori error estimator for defeaturing problems

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

A Local Law for Singular Values from Diophantine Equations

Nonlinear Finite Elements in Dynamics

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

An equilibrated flux a posteriori error estimator for defeaturing problems

Spectral Estimators for High-Dimensional Matrix Inference

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

A Local Law for Singular Values from Diophantine Equations

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Nonlinear Finite Elements in Dynamics