| Issue |
ESAIM: M2AN
Volume 53, Number 2, March-April 2019
|
|
|---|---|---|
| Page(s) | 475 - 501 | |
| DOI | https://doi.org/10.1051/m2an/2018066 | |
| Published online | 24 April 2019 | |
Anisotropic polygonal and polyhedral discretizations in finite element analysis
Department of Mathematics, Saarland University, 66041 Saarbrücken, Germany
* Corresponding author: weisser@num.uni-sb.de
Received:
14
November
2017
Accepted:
28
October
2018
Interpolation and quasi-interpolation operators of Clément- and Scott-Zhang-type are analyzed on anisotropic polygonal and polyhedral meshes. Since no reference element is available, an appropriate linear mapping to a reference configuration plays a crucial role. A priori error estimates are derived respecting the anisotropy of the discretization. Finally, the found estimates are employed to propose an adaptive mesh refinement based on bisection which leads to highly anisotropic and adapted discretizations with general element shapes in two- and three-dimensions.
Mathematics Subject Classification: 65D05 / 65N15 / 65N30 / 65N50
Key words: Anisotropic finite elements / polyhedral mesh / interpolation / error estimate / mesh adaptation
© EDP Sciences, SMAI 2019
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