[petsc-users] coordinate degrees of freedom for 2nd-order gmsh mesh

[Jed Brown]

Dave May <dave.mayhem23 at gmail.com> writes:

> On Thu 12. Jan 2023 at 17:58, Blaise Bourdin <bourdin at mcmaster.ca> wrote:
>
>> Out of curiosity, what is the rationale for _reading_ high order gmsh
>> meshes?
>>
>
> GMSH can use a CAD engine like OpenCascade. This provides geometric
> representations via things like BSplines. Such geometric representation are
> not exposed to the users application code, nor are they embedded in any
> mesh format GMSH emits. The next best thing is to use a high order
> representation of the mesh geometry and project the CAD geometry (say a
> BSpline) into this higher order function space. The projection of the
> geometry is a quantity that can be described with the .msh format.

Adding to this, efficient methods for volumes with concave surfaces *must* use at least quadratic geometry. See Figure 5, where "p-refinement with linear geometry" causes anti-convergence (due the spurious stress singularities from the linear geometry, visible in Figure 4) while p-refinement with quadratic geometry is vastly more efficient despite the physical stress singularities that prevent exponential convergence. 

https://arxiv.org/pdf/2204.01722.pdf