Convection–diffusion equation
The convection-diffusion equation is a more general version of the scalar transport equation. It is a combination of the diffusion and convection (advection) equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection.
$${\displaystyle \frac{\partial c}{\partial t}}=\mathrm{\nabla }\cdot (D\mathrm{\nabla }c-\mathbf{v}c)+R$$

$${\displaystyle \frac{\partial c}{\partial t}}=\underset{\text{diffusion}}{\underbrace{\mathrm{\nabla }\cdot (D\mathrm{\nabla }c)}}-\stackrel{\text{convection}}{\overbrace{\underset{\text{advection}}{\underbrace{\mathrm{\nabla }\cdot (\mathbf{v}c)}}}}+\stackrel{\text{creation}}{\overbrace{\underset{\text{destruction}}{\underbrace{R}}}}$$

$\mathrm{\nabla }\cdot (D\mathrm{\nabla }c)$ is the contribution of diffusion.
$-\mathrm{\nabla }\cdot (\mathbf{v}c)$ is the contribution of convection or advection.
$R$ describes the creation or destruction of the quantity.

where
$c$ is the variable of interest.
$D$ is the diffusivity.
$\mathbf{v}$ is the velocity field, and
$R$ is the sources or sinks of the quantity $c$.

An example of an error indicator is driven non-conforming mesh adaptivity for #advection problem using upwind high order #DG. Wind velocity is discretised by vector potential function in H1 one space. #MOFEM can do very cool things. That technology is implemented for 2d/3d problems. #FEM #FEA #HPC

Example #code is here:
http://mofem.eng.gla.ac.uk/mofem/html/tutorial_level_set.html

Our new paper on modelling the #spatiotemporal dynamics of a beneficial genetic variant is out @eLife.
Muktupavela et al: https://elifesciences.org/articles/73767
Plus a digest highlight here: https://elifesciences.org/digests/73767/evolving-through-time-and-space

We extend a #diffusion method for inferring the spread of a strongly selected allele, originally developed by Novembre et al. (https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0030339). We now incorporate #ancientDNA and allow for #advection dynamics.