Publications related to An Anisotropic Error Estimator For The Crank-Nicolson Method: Application To A Parabolic Problem

Related publications (29)

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

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

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

Paride Passelli

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 ...

EPFL2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

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

Stability: a search for structure

Wouter Jongeneel

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 ...

EPFL2024

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

Pakshal Narendra Bohra

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 ...

EPFL2024

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

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

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 ...

Springer2024

Modeling friction and wear using an adaptive discrete-continuum coupling

Manon Eugénie Voisin--Leprince

When two objects slide against each other, wear and friction occur at their interface. The accumulation of wear forms what is commonly referred to as a ``third-body''. Understanding third-body evolution has significant applications in industry, where contr ...

EPFL2024

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

Jan Sickmann Hesthaven, Niccolo' Discacciati

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 ...

Elsevier Science Sa2024

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

Maude Girardin, Marco Picasso, Alexandre Caboussat

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 ...

Elsevier Science Sa2024

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Gianluigi Rozza, Fabio Zoccolan

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Orientation-dependent two-dimensional magnonic crystal modes in an ultralow-damping ferrimagnetic waveguide containing repositioned hexagonal lattices of Cu disks

Dirk Grundler

Two-dimensional (2D) hexagonal lattices of Cu disks are shown to induce orientation-dependent magnonic crystal (MC) modes for propagating forward volume spin waves in a single-crystal yttrium iron garnet (YIG) film. The width and depth of the magnonic band ...

American Physical Society (APS)2024

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

Guillaume Michel Le Bars, Stefano Alberti, Jean-Philippe Hogge, Joaquim Loizu Cisquella, Jérémy Genoud, Francesco Romano

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 ...

2024

Anthony C Davison and Igor Rodionov's contribution to the Discussion of 'Estimating means of bounded random variables by betting' by Waudby-Smith and Ramdas

Igor Rodionov, Anthony Christopher Davison

We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and ...

Oxford Univ Press2024

A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects

Marco Picasso, Alexandre Caboussat, Alexandre Masserey, Julien Hess

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...

Academic Press Inc Elsevier Science2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini

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

A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces

Alfio Quarteroni, Andrea Manzoni

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...

Springer/Plenum Publishers2024

An equilibrated flux a posteriori error estimator for defeaturing problems

Annalisa Buffa, 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

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Marco Picasso, Samuel Dubuis

A space-time adaptive algorithm is presented to solve the incompressible Navier-Stokes equations. Time discretization is performed with the BDF2 method while continuous, piecewise linear anisotropic finite elements are used for the space discretization. Th ...

Academic Press Inc Elsevier Science2023

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Alfio Quarteroni, Francesca Bonizzoni

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Elsevier Science Sa2023

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Michaël Unser, Pakshal Narendra Bohra, Pol del Aguila Pla

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

2023