Concept
Elliptic operator
Related publications (124)
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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 ...
EPFL2024Anomalous dissipation and other non-smooth phenomena in fluids
The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...
EPFL2024THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...
Philadelphia2023Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds
Le Chen, Cheuk Yin Lee, David Jean-Michel Candil
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...
New York2023Essays in macro-finance and deep learning
This thesis studies the origins and consequences of financial crises, and computational techniques to solve continuous-time economic models that explain such crises. The first chapter shows that financial recessions are typically characterised by a large r ...
EPFL2023