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.

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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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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