# what is the difference between non-conformal and conformal?

So far what I understand is that two neighbouring elements are conformal if their edges and faces match exactly, whereas with non-conformal elements this is not the case. For instance, h-refinement gives rise to hanging nodes, and h-nonconforming elements.

But then there is the concept of p-nonconforming. Note sure, but I think this applies for instance in DGFEM, where the weight functions are the roots of a polynomial and which do not match at the boundaries?

I would appreciate it if someone offered a simple explanation for this, particularly in the context of typical structured grids used in DGFEM, FEM and FVM.

The concept of $p$-nonconforming meshes can also apply to continuous FEM, not just DG. For continuous FEM, continuity is enforced by enforcing a single set of degrees of freedom on a face shared between two elements. If those elements have varying polynomial degrees, the trace space on the face must be made the same. This may be done by restricting the higher degree element to a lower degree trace (referred to as the minimum rule) or by increasing the degree of the trace space for the lower degree element (referred to as the maximum rule).
For DG, $p$-nonconforming meshes are much simpler to implement, as elements are coupled together weakly through a unique interface flux. The method behaves is pretty much identically so long as the computation of integrals of this flux are computed with sufficiently accurate quadrature (though implementation details may change between uniform $p$ and variable $p$ codes).
I'm less familiar with FVM, but I think $p$-nonconformity may depend on what type of high $p$ FVM you use (wider stencil, compact/multi-resolution, etc).
• It depends - they can be referring to $h$-nonconformity for DG as well. In both $h$ and $p$ nonconformity, the basis functions at faces don't match and some work has to be done to pair them. Commented Dec 1, 2015 at 17:58