Section: New Results

Assessment of the discontinuous Galerkin methods on curved meshes

The internship of Hamza Belkhayat-Zougari was concerned with the handling of high order curved meshes in the Aerosol library. During his internship, we developed new analytical solutions of the Laplace and of the Navier-Stokes equations on curved domains for emphasizing the limitation at second order of high order methods on straight meshes, and for assessing the right order on high order meshes. Example of order obtained on straight and curved meshes can be found on Figure 5 .

Figure 5. Convergence on a ring for the Laplace equation. Left: high order method on a straight mesh is limited to two. Right: third order accuracy can be recovered by using a second order mesh.