We consider a family of quadrilateral or hexahedral mixed -finite elements for an incompressible flow problem with -elements for the velocity and discontinuous -elements for the pressure where the order can vary from element to element between 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.
Keywords: Stokes problem, inf-sup condition, mixed $hp$-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes
@article{M2AN_2008__42_3_493_0, author = {Schieweck, Friedhelm}, title = {Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {493--505}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/m2an:2008014}, mrnumber = {2423796}, zbl = {1154.76034}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008014/} }
TY - JOUR AU - Schieweck, Friedhelm TI - Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 493 EP - 505 VL - 42 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008014/ DO - 10.1051/m2an:2008014 LA - en ID - M2AN_2008__42_3_493_0 ER -
%0 Journal Article %A Schieweck, Friedhelm %T Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 493-505 %V 42 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008014/ %R 10.1051/m2an:2008014 %G en %F M2AN_2008__42_3_493_0
Schieweck, Friedhelm. Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 3, pp. 493-505. doi : 10.1051/m2an:2008014. http://www.numdam.org/articles/10.1051/m2an:2008014/
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