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LUCiFEx Demo

User Guide

Introductory

Notation
Poisson equation
Diffusion equation
- Diffusion of a Gaussian in an interval
- Diffusion of a Gaussian in a rectangle
Advection equation
- Advection of a Gaussian in an interval
Advection-diffusion equation
- Advection-diffusion of a Gaussian in an interval
Helmholtz equation
- Helmholtz eigenvalue problem in a rectangle
- Helmholtz boundary value problem in a rectangle
Mathieu equation
- Mathieu eigenvalue problem in an interval

Fluids

Notation
Darcy equations
Stokes equations
Navier-Stokes equations
- Flow of Navier-Stokes fluid past a circular obstacle
- Flow of a Navier-Stokes fluid with vertical forcing

Transport

DG formulation of the advection equation
DG formulation of the steady advection-diffusion-reaction equation
- DG steady advection-diffusion in an interval
- DG steady advection-diffusion in a rectangle
DG formulation of the advection-diffusion-reaction equation
- DG advection-diffusion of a tophat on an interval
- DG advection-diffusion in a rectangle
SUPG stabilization of the steady advection-diffusion-reaction equation
SUPG stabilization of the advection-diffusion-reaction equation
- SUPG advection-diffusion of a Gaussian in an interval
- SUPG advection-diffusion of a rotating pulse in a rectangle

Convection

Darcy convection equations
Stokes convection equations
- Rayleigh-Bénard convection of an isoviscous Stokes fluid
- Rayleigh-Bénard convection of a non-isoviscous Stokes fluid
Navier-Stokes convection equations

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By The Jupyter Book community