Anisotropic Meshes for Resolving Edge Singularities and Boundary Layers
Thomas Apel (TU Chemnitz)
Anisotropic meshes are characterized by elements with a large or even
asymptotically unbounded aspect ratio. Such meshes are known to be
particularly effective for the resolution of directional features of
the solution. In the talk, we characterize suitable anisotropic
meshes for approximating edge singularities in various elliptic
problems and boundary layers in singularly perturbed problems.
In solving the Stokes or Navier-Stokes problem the question arises
which pairs of elements are stable independent of the aspect ratio of
the elements. For several pairs of elements positive and negative
results are given.