Publications associées à Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Publications associées (30)

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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 ...

Siam Publications2024

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

An Adaptive Least-squares Algorithm for the Elliptic Monge-ampere Equation

Dimitrios Gourzoulidis

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearitie ...

ACAD SCIENCES2023

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Boris Buffoni

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

Guillaume Anciaux, Simone Deparis, Yannis Dirk Voet

The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, ...

PERGAMON-ELSEVIER SCIENCE LTD2022

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Annalisa Buffa, Rafael Vazquez Hernandez

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these result ...

Springer2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Johanni Michael Brea, Jean-Pascal Théodor Pfister

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020

Preferential retention of algal carbon in benthic invertebrates: Stable isotope and fatty acid evidence from an outdoor flume experiment

Tom Ian Battin

According to the River Continuum Concept, headwater streams are richer in allochthonous (e.g. terrestrial leaves) than autochthonous (e.g. algae) sources of organic matter for consumers. However, compared to algae, leaf litter is of lower food quality, par ...

WILEY2020

On the equation A del u plus (del u)(t) A = G

Bernard Dacorogna, David Valentin Strütt

Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates

Luigi Forcella

We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...

2021

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

A cellulolytic fungal biofilm enhances the consolidated bioconversion of cellulose to short chain fatty acids by the rumen microbiome

Robert Lawrence Shahab

The ability of the multispecies biofilm membrane reactors (MBM reactors) to provide distinguished niches for aerobic and anaerobic microbes at the same time was used for the investigation of the consolidated bioprocessing of cellulose to short chain fatty ...

2019

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

Fabio Nobile, Eleonora Musharbash

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational ...

Elsevier2018

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Clément Hongler, Franck Raymond Gabriel, Arthur Ulysse Jacot-Guillarmod

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

Multi space reduced basis preconditioners for large-scale parametrized PDEs

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, whi ...

2018

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...

MATHICSE2018