07-02
Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
Preprint series: 07-02, Preprints
- MSC:
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65N35 Spectral, collocation and related methods
- 76D07 Stokes flows
Abstract: 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.
Keywords: Stokes problem, inf-sup condition, mixed hp-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes
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