On 4/25/19 2:50 PM, Gary Uppal wrote: > > I am trying to solve the diffusion equation with Discontinuous Galerkin > elements. The solution looks good with a regular structured mesh, but if I > distort the mesh, the solution blows up and does not converge. Is there an > obvious reason this would happen? I later need a mesh with holes in it, so I > cannot always use the structured mesh. > > I use the interior penalty method and get the diffusion matrix using > MeshWorker as in Step-39. I compute the mass matrix and solve the diffusion > equation with an implicit backward Euler method and am using periodic > boundary > conditions. Snapshots of the solution with structured and distorted meshes > are > shown below. Any help is appreciated!
Gary -- the wrong solutions happen on cells that are very nearly degenerate (i.e., are almost triangular). The finite element theory says that the error between the exact and the numerical solution is bounded by a constant times some power of h, where the constant depends on the minimal and maximal angles at the vertices of the cells. Theory then also predicts that this constant goes to infinity if the maximal angle at one vertex comes close to 180 degrees -- which is exactly what is happening in your case. So choose a mesh that is less distorted and you should be fine. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- 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 [email protected]. For more options, visit https://groups.google.com/d/optout.
