Geodesic
Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 493-505

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We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Q r -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.

DOI : 10.1051/m2an:2008014
Classification : 65N30, 65N35, 76D07
Keywords: Stokes problem, inf-sup condition, mixed $hp$-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes 
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     title = {Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an:2008014/}
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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 , Tome 42 (2008) no. 3, pp. 493-505. doi: 10.1051/m2an:2008014

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