Praveen, > I need to use the cell size h in the dissipation term of a DG scheme. For > adapted grids or non-uniform grids, the cell size varies in a discontinuous > way, which affects the solution, since now the numerical dissipation varies > in a discontinuous way. Is there any simple way to construct a smoother > function h(x) which gives the cell size variation.
Not easily. Essentially, what you ask for is this: given a function H(x), find me a mesh whose mesh size function is h(x) \approx H(x). First, it is clear that h(x)=H(x) is not in general possible since for any mesh h(x) is a piecewise constant function, so the equality could in principle only hold if H(x) is also piecewise constant. But more generally, this is again not a trivial problem. Imagine, for example, a function H(x) that that is so that it has very large values right next to very small values. You won't be able to find a mesh that can satisfy this since the maximal jump in h(x) from one cell to the next is by a factor of two if you start from a coarse mesh in which all cells have the same size. Furthermore, for such adaptively refined meshes, h(x) is either equal on two neighboring cells, or differs by a factor of 2. You seem to imply that this jump in mesh size is too large. Since adaptively refined meshes can't do anything smaller, your only choice is to use a non- adaptively refined mesh (i.e. what we would call a "coarse mesh") that satisfies your target function H(x). deal.II can't generate such meshes itself, but some mesh generators give it a good try. I believe gmsh, for example, allows you to specify a function H(x) and it then tries its best to find a mesh so that h(x) \approx H(x). Give that a try. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
