Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes

Friedhelm Schieweck

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 3, page 493-505
  • ISSN: 0764-583X

Abstract

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We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous P r - 1 -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.

How to cite

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Schieweck, Friedhelm. "Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes." ESAIM: Mathematical Modelling and Numerical Analysis 42.3 (2008): 493-505. <http://eudml.org/doc/250391>.

@article{Schieweck2008,
abstract = { We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous $P_\{r-1\}$-elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree. },
author = {Schieweck, Friedhelm},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Stokes problem; inf-sup condition; mixed hp-FEM; quadrilateral and hexahedral finite elements; multilevel adaptive grids; hanging nodes.; quadrilateral element; hexahedral element},
language = {eng},
month = {4},
number = {3},
pages = {493-505},
publisher = {EDP Sciences},
title = {Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes},
url = {http://eudml.org/doc/250391},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Schieweck, Friedhelm
TI - Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/4//
PB - EDP Sciences
VL - 42
IS - 3
SP - 493
EP - 505
AB - We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous $P_{r-1}$-elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
LA - eng
KW - Stokes problem; inf-sup condition; mixed hp-FEM; quadrilateral and hexahedral finite elements; multilevel adaptive grids; hanging nodes.; quadrilateral element; hexahedral element
UR - http://eudml.org/doc/250391
ER -

References

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