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Table
Notation

Introductory

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
- Advection-diffusion of a Gaussian in a rectangle
Helmholtz equation
- Helmholtz eigenvalue problem in a rectangle
- Helmholtz boundary value problem in a rectangle
Mathieu equation
- Mathieu eigenvalue problem in an interval
Wave equation
- Wave equation in an interval
Other boundary conditions
Spatial and temporal resolution
- Steady diffusion-reaction with mesh refinement
- Poisson equation with method of manufactured solutions

Transport

DG methods for the advection equation
DG methods for the steady advection-diffusion-reaction equation
- DG steady advection-diffusion-reaction with a skew velocity
DG methods for 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-reaction of a rotating pulse in a rectangle
Splitting methods for the transport equation
- Splitting method for the advection-reaction equation
Predictor-corrector methods for the transport equation
- Predictor-corrector method for the advection-diffusion equation

Flow

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
Darcy-Brinkman equations
- Flow of a Darcy-Brinkman fluid past a permeable obstacle

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
Darcy-Brinkman convection equations
- Rayleigh-Bénard convection of a Darcy-Brinkman fluid in a partially porous rectangle

Further Applications

Darcy fingering equations
Darcy ABC convection-reaction equations
- ABC convection of a Darcy fluid in a porous rectangle

Benchmarks

Rayleigh-Bénard convection benchmark
Taylor-Green vortex benchmark

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Other boundary conditions

Other boundary conditions#

time-dependent boundary conditions
periodic boundary conditions
Nitsche boundary conditions

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Wave equation in an interval

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Diffusion-reaction equation with time-dependent Dirichlet boundary conditions

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