One-dimensional linear advection-diffusion equation: Analytical and finite element solutions

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

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 ...

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 ...

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 ...

We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamics equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and probabilistic ar ...

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 ...

Genes implicated in translation control have been associated with autism spectrum disorders (ASDs). However, some important genetic causes of autism, including the 16p11.2 microdeletion, bear no obvious connection to translation. Here, we use proteomics, g ...

The Obukhov-Corrsin theory of scalar turbulence [21, 54] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully developed turbulence [4 ...

In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

The dorsomedial prefrontal cortex/dorsal anterior cingulate cortex (dmPFC/dACC) is a brain area subject to many theories and debates over its function(s). Even its precise anatomical borders are subject to much controversy. In the past decades, the dmPFC/d ...

We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The permutations of vertex ...

In impermeable media, a hydraulic fracture can continue to expand even without additional fluid injection if its volume exceeds the limiting volume of a hydrostatically loaded radial fracture. This limit depends on the mechanical properties of the surround ...

We prove that every online learnable class of functions of Littlestone dimension d admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of ...

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

The energy Casimir method is an effective controller design approach to stabilize port-Hamiltonian systems at a desired equilibrium. However, its application relies on the availability of suitable Casimir and Lyapunov functions, whose computation are gener ...

Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...

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 ...

The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...

The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...

Semi-Lagrangian (SL) schemes are of utmost relevance to simulate two-phase flows where advection dominates. The combination of SL schemes with the finite element (FE) method and arbitrary Lagrangian-Eulerian (ALE) dynamic meshes yields a strong ingredient ...

One-dimensional linear advection-diffusion equation: Analytical and finite element solutions

Chattez avec Graph Search

Anomalous dissipation and other non-smooth phenomena in fluids

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

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

Quantitative convergence rates for scaling limit of SPDEs with transport noise

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

The autism susceptibility kinase, TAOK2, phosphorylates eEF2 and modulates translation

Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence

Algebraic twists of GL(2) automorphic forms

Stable parameterization of continuous and piecewise-linear functions

Debates on the dorsomedial prefrontal/dorsal anterior cingulate cortex: insights for future research

Symmetry and Invariant Bases in Finite Element Exterior Calculus

Three-dimensional buoyant hydraulic fractures: finite volume release

Finite Littlestone Dimension Implies Finite Information Complexity

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Neural Energy Casimir Control for Port-Hamiltonian Systems

Blow-up, partial regularity and turbulence in incompressible fluid dynamics

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

Reduced basis methods for numerical room acoustic simulations with parametrized boundaries

Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete

One- and two-step semi-Lagrangian integrators for arbitrary Lagrangian-Eulerian-finite element two-phase flow simulations