Displaying similar documents to “On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes”

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

Friedhelm Schieweck (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a family of quadrilateral or hexahedral mixed -finite elements for an incompressible flow problem with -elements for the velocity and discontinuous P r - 1 -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.

Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra

Gunar Matthies (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present families of scalar nonconforming finite elements of arbitrary order r ≥ 1 with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order r - 1 form inf-sup stable finite element pairs of order for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case . A numerical comparison between conforming and nonconforming discretisations will be given. Since...

A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

Malte Braack (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...

Some mixed finite element methods on anisotropic meshes

Mohamed Farhloul, Serge Nicaise, Luc Paquet (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some...