TY - JOUR
T1 - Design of Finite Element Tools for Coupled Surface and Volume Meshes
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 245
EP - 274
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6051.html
KW - Adaptive finite element methods, scientific software, software design.
AB - <p style="text-align: justify;">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 &quot;matching&quot; 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.</p>