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

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

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

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

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

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 Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

Convergence To Stratified Flow For An Inviscid 3D Boussinesq System

Klaus Martin Widmayer

We study the stability of special, stratified solutions of a 3D Boussinesq system describing an incompressible, inviscid 3D fluid with variable density (or temperature, depending on the context) under the effect of a uni-directional gravitational force. Th ...

INT PRESS BOSTON, INC2018

Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations

Maria Colombo, Luigi De Rosa, Camillo De Lellis

We prove the ill-posedness of Leray solutions to the Cauchy problem for the hypodissipative Navier-Stokes equations, when the dissipative term is a fractional Laplacian with exponent . The proof follows the "convex integration methods" introduced by the se ...

2018

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear esti ...

IEEE2018

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

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

Elsevier2017

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...

MATHICSE2017

MATHICSE Technical Report : A posteriori error estimation for the steady Navier-Stokes equations in random domains

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

Nonlinear Finite Elements in Dynamics

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

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Convergence To Stratified Flow For An Inviscid 3D Boussinesq System

Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

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

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

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

Nonlinear Finite Elements in Dynamics

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

A Local Law for Singular Values from Diophantine Equations

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Convergence To Stratified Flow For An Inviscid 3D Boussinesq System

Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations

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