On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes

Vincent Heuveline; Friedhelm Schieweck

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 1, page 1-20
  • ISSN: 0764-583X

Abstract

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We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations 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 a fixed bound r * . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.

How to cite

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Heuveline, Vincent, and Schieweck, Friedhelm. "On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 1-20. <http://eudml.org/doc/250031>.

@article{Heuveline2007,
abstract = { We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations 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 a fixed bound $r^*$. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes. },
author = {Heuveline, Vincent, Schieweck, Friedhelm},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Inf-sup condition; higher order mixed finite element; adaptive grids; hanging nodes.; inf-sup condition; adaptive grids; hanging nodes; stability; Stokes equations},
language = {eng},
month = {4},
number = {1},
pages = {1-20},
publisher = {EDP Sciences},
title = {On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes},
url = {http://eudml.org/doc/250031},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Heuveline, Vincent
AU - Schieweck, Friedhelm
TI - On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 1
EP - 20
AB - We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations 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 a fixed bound $r^*$. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.
LA - eng
KW - Inf-sup condition; higher order mixed finite element; adaptive grids; hanging nodes.; inf-sup condition; adaptive grids; hanging nodes; stability; Stokes equations
UR - http://eudml.org/doc/250031
ER -

References

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