## Chapter 5

Summary

You should be now familiar with the following topics:

- Generate a simple mesh in Gmsh and convert it in a Nektar++-compatible format;
- Visualise the mesh in Paraview;
- Setup the boundary conditions, the parameters and the solver settings;
- Run the ADR solver; and
- Post-process the data in order to visualise results in Paraview/VisIt.

### 5.1 Additional Exercises

- Increase the polynomial order and plot the L
_{2} error vs. the polynomial order in a
semilogarithmic scale.
- If the solver is compiled with the MPI option, then try running the case in parallel
with
`mpirun -np 2`

.
- Change the Projection Operator to DisContinuous to see the same problem running
with an HDG solver.
- Change one of the boundary conditiosn to a Robin (Mixed) boundary condition of
the form ∂u∕∂n = αu + β whith α = 1 and β determined from the exact solution.

**Tip:** To check the additional settings and parameters that can be used for this solver, check
the folder: `$NEK/solvers/ADRSolver/Tests/`

where you can find several tests associated to
the ADR solver.