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

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

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topSchieweck, 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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