Volume 1, Issue 3
Design of Finite Element Tools for Coupled Surface and Volume Meshes

Daniel Köster, Oliver Kriessl & Kunibert G. Siebert

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 245-274.

Published online: 2008-01

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  • 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.

  • Keywords

Adaptive finite element methods, scientific software, software design.

  • AMS Subject Headings

65N30, 65N50, 65Y15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-245, author = {}, title = {Design of Finite Element Tools for Coupled Surface and Volume Meshes}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {3}, pages = {245--274}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6051.html} }
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 -

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.

Daniel Köster, Oliver Kriessl & Kunibert G. Siebert. (2020). Design of Finite Element Tools for Coupled Surface and Volume Meshes. Numerical Mathematics: Theory, Methods and Applications. 1 (3). 245-274. doi:
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