Anisotropic polygonal and polyhedral discretizations in finite element analysis
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 2, pp. 475-501.

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018066
Classification : 65D05, 65N15, 65N30, 65N50
Mots-clés : Anisotropic finite elements, polyhedral mesh, interpolation, error estimate, mesh adaptation
Weißer, Steffen 1

1 
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     title = {Anisotropic polygonal and polyhedral discretizations in finite element analysis},
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Weißer, Steffen. Anisotropic polygonal and polyhedral discretizations in finite element analysis. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 2, pp. 475-501. doi : 10.1051/m2an/2018066. http://www.numdam.org/articles/10.1051/m2an/2018066/

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