Hello, I am not sure if FE_DGP and FE_DGPMonomial is behaving as expected.
I had recently commented on a thread about distorted meshes ( https://groups.google.com/forum/#!topic/dealii/ZSHIDbp7yfE). I am using DG to solve a linear advection problem with a manufactured solution. A 2D square with perfectly straight cartesian elements, MappingQ, FE_DGP (Legendre polynomials), would give me optimal (p+1) order of convergence with h-refinement. However, if the h-refinement is followed by a small random distortion through (distort_random), the optimal convergence is lost. If a distorted mesh is h-refined subsequently (such that the distortion is only on the coarse grid), then optimal convergence orders are achieved. As Prof. Bangerth mentionned, this refinement results in elements that tend to parallelograms, which have a linear Jacobian. Now, if I use FE_DGQ (tensor Lagrange) or FE_DGQLegendre (tensor-product Legendre), I do obtain optimal orders of convergence, no matter the distortion. Based on this, I assume that FEValues, which takes a FiniteElement and a Mapping, uses them to evaluate the Jacobian field instead of using a bilinear mapping as the documentation of Mapping suggests. So FE_DGP would only be able to parametrize the cell geometry with the polynomial space {1, x, y} instead of {1, x, y, xy}. The documentation of FE_DGP does mention similar to this, but I thought this only applied to the solution, not the geometric mapping. I would expect the geometric mapping to always use a tensor product basis in order to be able to represent any straight-sided quads, especially since deal.II only handles quads. Since the FEValues seems to evaluate Jacobian based on the provided FiniteElement, FE_DGP is basically useless since it can only handle truly linear elements. It's not really an issue for me since I will just switch to a tensor-product basis. However, I am curious whether or not my understanding of what is happening is correct, and if this behaviour is expected. Best Regards, Doug -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
