Abstract
Many problems with underlying variational structure involve a coupling
of volume with surface effects. A straight-forward approach in a
finite element discretization is to make use of the surface triangulation
that is naturally induced by the volume triangulation. In an adaptive
method one wants to facilitate "matching" local mesh modifications,
i.e., local refinement and/or coarsening, of volume and surface mesh
with standard tools such that the surface grid is always induced
by the volume grid. We describe the concepts behind this approach
for bisectional refinement and describe new tools incorporated in
the finite element toolbox ALBERTA. We also present several important
applications of the mesh coupling.
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