Optimal finite-element interpolation on curved domains
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Journal of Computational and Applied Mathematics
Adaptive Finite Element Methods on Quadrilateral Meshes without Hanging Nodes
SIAM Journal on Scientific Computing
New robust nonconforming finite elements of higher order
Applied Numerical Mathematics
The two-level local projection stabilization as an enriched one-level approach
Advances in Computational Mathematics
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One of the most popular pairs of finite elements for solving mixed formulations of the Stokes and Navier-Stokes problem is the Qk - Pk-1disc element. Two possible versions of the discontinuous pressure space can be considered: one can either use an unmapped version of the Pk-1disc space consisting of piecewise polynomial functions of degree at most k - 1 on each cell or define a mapped version where the pressure space is defined as the image of a polynomial space on a reference cell. Since the reference transformation is in general not affine but multilinear, the two variants are not equal on arbitrary meshes. It is well-known, that the inf-sup condition is satisfied for the first variant. In the present paper we show that the latter approach satisfies the inf-sup condition as well for k ≥ 2 in any space dimension.