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Fix rendering of some links in docs #1620

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Fix rendering of some links in docs #1620

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2 changes: 1 addition & 1 deletion docs/literate/src/files/differentiable_programming.jl
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Expand Up @@ -128,7 +128,7 @@ condition_number = cond(V)
# you can compute the gradient of an entropy-dissipative semidiscretization with respect to the
# ideal gas constant of the compressible Euler equations as described in the following. This example
# is also available as the elixir
# [examples/special\_elixirs/elixir\_euler\_ad.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/special_elixirs/elixir_euler_ad.jl)
# [`examples/special_elixirs/elixir_euler_ad.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/special_elixirs/elixir_euler_ad.jl)

# First, we create a semidiscretization of the compressible Euler equations.

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2 changes: 1 addition & 1 deletion docs/literate/src/files/index.jl
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Expand Up @@ -116,7 +116,7 @@

# ## Examples in Trixi.jl
# Trixi.jl already contains several more coding examples, the so-called `elixirs`. You can find them
# in the folder [`examples`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/).
# in the folder [`examples/`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/).
# They are structured by the underlying mesh type and the respective number of spatial dimensions.
# The name of an elixir is composed of the underlying system of conservation equations (for instance
# `advection` or `euler`) and other special characteristics like the initial condition
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22 changes: 11 additions & 11 deletions docs/src/callbacks.md
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Expand Up @@ -15,7 +15,7 @@ control, adaptive mesh refinement, I/O, and more.

### CFL-based time step control
Time step control can be performed with a [`StepsizeCallback`](@ref). An example making use
of this can be found at [examples/tree_2d_dgsem/elixir\_advection\_basic.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_basic.jl)
of this can be found at [`examples/tree_2d_dgsem/elixir_advection_basic.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_basic.jl)

### Adaptive mesh refinement
Trixi.jl uses a hierarchical Cartesian mesh which can be locally refined in a solution-adaptive way.
Expand All @@ -24,12 +24,12 @@ passing an [`AMRCallback`](@ref) to the ODE solver. The `AMRCallback` requires a
[`ControllerThreeLevel`](@ref) or [`ControllerThreeLevelCombined`](@ref) to tell the AMR
algorithm which cells to refine/coarsen.

An example elixir using AMR can be found at [examples/tree_2d_dgsem/elixir\_advection\_amr.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_amr.jl).
An example elixir using AMR can be found at [`examples/tree_2d_dgsem/elixir_advection_amr.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_amr.jl).

### Analyzing the numerical solution
The [`AnalysisCallback`](@ref) can be used to analyze the numerical solution, e.g. calculate
errors or user-specified integrals, and print the results to the screen. The results can also be
saved in a file. An example can be found at [examples/tree_2d_dgsem/elixir\_euler\_vortex.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_euler_vortex.jl).
saved in a file. An example can be found at [`examples/tree_2d_dgsem/elixir_euler_vortex.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_euler_vortex.jl).
In [Performance metrics of the `AnalysisCallback`](@ref) you can find a detailed
description of the different performance metrics the `AnalysisCallback` computes.

Expand All @@ -38,15 +38,15 @@ description of the different performance metrics the `AnalysisCallback` computes
#### Solution and restart files
To save the solution in regular intervals you can use a [`SaveSolutionCallback`](@ref). It is also
possible to create restart files using the [`SaveRestartCallback`](@ref). An example making use
of these can be found at [examples/tree_2d_dgsem/elixir\_advection\_extended.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_extended.jl).
of these can be found at [`examples/tree_2d_dgsem/elixir_advection_extended.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_extended.jl).
An example showing how to restart a simulation from a restart file can be found at
[examples/tree_2d_dgsem/elixir\_advection\_restart.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_restart.jl).
[`examples/tree_2d_dgsem/elixir_advection_restart.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_restart.jl).

#### Time series
Sometimes it is useful to record the evaluations of state variables over time at
a given set of points. This can be achieved by the [`TimeSeriesCallback`](@ref), which is used,
e.g., in
[examples/tree_2d_dgsem/elixir\_acoustics\_gaussian\_source.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl).
[`examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl).
The `TimeSeriesCallback` constructor expects a semidiscretization and a list of points at
which the solution should be recorded in regular time step intervals. After the
last time step, the entire record is stored in an HDF5 file.
Expand Down Expand Up @@ -113,12 +113,12 @@ will yield the following plot:
Some callbacks provided by Trixi.jl implement specific features for certain equations:
* The [`LBMCollisionCallback`](@ref) implements the Lattice-Boltzmann method (LBM) collision
operator and should only be used when solving the Lattice-Boltzmann equations. See e.g.
[examples/tree_2d_dgsem/elixir\_lbm\_constant.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_lbm_constant.jl)
[`examples/tree_2d_dgsem/elixir_lbm_constant.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_lbm_constant.jl)
* The [`SteadyStateCallback`](@ref) terminates the time integration when the residual steady state
falls below a certain threshold. This checks the convergence of the potential ``\phi`` for
hyperbolic diffusion. See e.g. [examples/tree_2d_dgsem/elixir\_hypdiff\_nonperiodic.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl).
hyperbolic diffusion. See e.g. [`examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl).
* The [`GlmSpeedCallback`](@ref) updates the divergence cleaning wave speed `c_h` for the ideal
GLM-MHD equations. See e.g. [examples/tree_2d_dgsem/elixir\_mhd\_alfven\_wave.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl).
GLM-MHD equations. See e.g. [`examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl).

## Usage of step callbacks
Step callbacks are passed to the `solve` method from the ODE solver via the keyword argument
Expand Down Expand Up @@ -152,7 +152,7 @@ more callbacks, you need to turn them into a `CallbackSet` first by calling
## Stage callbacks
[`PositivityPreservingLimiterZhangShu`](@ref) is a positivity-preserving limiter, used to enforce
physical constraints. An example elixir using this feature can be found at
[examples/tree_2d_dgsem/elixir\_euler\_positivity.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_euler_positivity.jl).
[`examples/tree_2d_dgsem/elixir_euler_positivity.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_euler_positivity.jl).

## Implementing new callbacks
Since Trixi.jl is compatible with [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl),
Expand All @@ -162,4 +162,4 @@ Step callbacks are just called [callbacks](https://diffeq.sciml.ai/latest/featur
Stage callbacks are called [`stage_limiter!`](https://diffeq.sciml.ai/latest/solvers/ode_solve/#Explicit-Strong-Stability-Preserving-Runge-Kutta-Methods-for-Hyperbolic-PDEs-(Conservation-Laws)).

An example elixir showing how to implement a new simple stage callback and a new simple step
callback can be found at [examples/tree_2d_dgsem/elixir\_advection\_callbacks.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_callbacks.jl).
callback can be found at [`examples/tree_2d_dgsem/elixir_advection_callbacks.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_callbacks.jl).
14 changes: 9 additions & 5 deletions docs/src/meshes/dgmulti_mesh.md
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Expand Up @@ -81,16 +81,20 @@ type, but will be more efficient at high orders of approximation.
## Trixi.jl elixirs on simplicial and tensor product element meshes

Example elixirs with triangular, quadrilateral, and tetrahedral meshes can be found in
the `examples/dgmulti_2d` and `examples/dgmulti_3d` folders. Some key elixirs to look at:
the [`examples/dgmulti_2d/`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/dgmulti_2d/)
and [`examples/dgmulti_3d/`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/dgmulti_3d/)
folders. Some key elixirs to look at:

* `examples/dgmulti_2d/elixir_euler_weakform.jl`: basic weak form DG discretization on a uniform triangular mesh.
* [`examples/dgmulti_2d/elixir_euler_weakform.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/dgmulti_2d/elixir_euler_weakform.jl):
basic weak form DG discretization on a uniform triangular mesh.
Changing `element_type = Quad()` or `approximation_type = SBP()` will switch to a quadrilateral mesh
or an SBP-type discretization. Changing `surface_integral = SurfaceIntegralWeakForm(flux_ec)` and
`volume_integral = VolumeIntegralFluxDifferencing(flux_ec)` for some entropy conservative flux
(e.g., [`flux_chandrashekar`](@ref) or [`flux_ranocha`](@ref)) will switch to an entropy conservative formulation.
* `examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl`: uses an unstructured mesh generated by
[Triangulate.jl](https://github.com/JuliaGeometry/Triangulate.jl).
* `examples/dgmulti_3d/elixir_euler_weakform.jl`: basic weak form DG discretization on a uniform tetrahedral mesh.
* [`examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl):
uses an unstructured mesh generated by [Triangulate.jl](https://github.com/JuliaGeometry/Triangulate.jl).
* [`examples/dgmulti_3d/elixir_euler_weakform.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/dgmulti_3d/elixir_euler_weakform.jl):
´basic weak form DG discretization on a uniform tetrahedral mesh.
Changing `element_type = Hex()` will switch to a hexahedral mesh. Changing
`surface_integral = SurfaceIntegralWeakForm(flux_ec)` and
`volume_integral = VolumeIntegralFluxDifferencing(flux_ec)` for some entropy conservative flux
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4 changes: 2 additions & 2 deletions docs/src/overview.md
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Expand Up @@ -5,7 +5,7 @@ conservation laws. Thus, it is not a monolithic PDE solver that is configured at
via parameter files, as it is often found in classical numerical simulation codes.
Instead, each simulation is configured by pure Julia code. Many examples of such
simulation setups, called *elixirs* in Trixi.jl, are provided in the
[examples](https://github.com/trixi-framework/Trixi.jl/blob/main/examples)
[`examples/`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples)
folder.

Trixi.jl uses the method of lines, i.e., the full space-time discretization is separated into two steps;
Expand Down Expand Up @@ -77,7 +77,7 @@ Further information can be found in the
## Next steps

We explicitly encourage people interested in Trixi.jl to have a look at the
[examples](https://github.com/trixi-framework/Trixi.jl/blob/main/examples)
[`examples/`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples)
bundled with Trixi.jl to get an impression of what is possible and the general
look and feel of Trixi.jl.
Before doing that, it is usually good to get an idea of
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10 changes: 5 additions & 5 deletions docs/src/restart.md
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Expand Up @@ -18,15 +18,15 @@ save_restart = SaveRestartCallback(interval=100,
Make this part of your `CallbackSet`.

An example is
[```examples/examples/structured_2d_dgsem/elixir_advection_extended.jl```](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/structured_2d_dgsem/elixir_advection_extended.jl).
[`examples/examples/structured_2d_dgsem/elixir_advection_extended.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/structured_2d_dgsem/elixir_advection_extended.jl).


## [Perform the simulation restart](@id restart_perform)
Since all of the information about the simulation can be obtained from the
last snapshot, the restart can be done with relatively few lines
in an extra elixir file.
However, some might prefer to keep everything in one elixir and
conditionals like ```if restart``` with a boolean variable ```restart``` that is user defined.
conditionals like `if restart` with a boolean variable `restart` that is user defined.

First we need to define from which file we want to restart, e.g.
```julia
Expand All @@ -50,7 +50,7 @@ time the one form the snapshot:
tspan = (load_time(restart_filename), 2.0)
```

We now also take the last ```dt```, so that our solver does not need to first find
We now also take the last `dt`, so that our solver does not need to first find
one to fulfill the CFL condition:
```julia
dt = load_dt(restart_filename)
Expand All @@ -63,7 +63,7 @@ ode = semidiscretize(semi, tspan, restart_filename)

You should now define a [`SaveSolutionCallback`](@ref) similar to the
[original simulation](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/structured_2d_dgsem/elixir_advection_extended.jl),
but with ```save_initial_solution=false```, otherwise our initial snapshot will be overwritten.
but with `save_initial_solution=false`, otherwise our initial snapshot will be overwritten.
If you are using one file for the original simulation and the restart
you can reuse your [`SaveSolutionCallback`](@ref), but need to set
```julia
Expand All @@ -86,4 +86,4 @@ Now we can compute the solution:
sol = solve!(integrator)
```

An example is in `[``examples/structured_2d_dgsem/elixir_advection_restart.jl```](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/structured_2d_dgsem/elixir_advection_restart.jl).
An example is in [`examples/structured_2d_dgsem/elixir_advection_restart.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/structured_2d_dgsem/elixir_advection_restart.jl).
2 changes: 1 addition & 1 deletion docs/src/visualization.md
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Expand Up @@ -375,7 +375,7 @@ During the simulation, the visualization callback creates and displays
visualizations of the current solution in regular intervals. This can be useful
to, e.g., monitor the validity of a long-running simulation or for illustrative
purposes. An example for how to create a `VisualizationCallback` can be found in
[examples/tree\_2d\_dgsem/elixir\_advection\_amr\_visualization.jl](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl):
[`examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl`](https://github.com/trixi-framework/Trixi.jl/blob/main/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl):
```julia
[...]

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