# Exact sequences on Powell–Sabin splits

@article{Guzmn2019ExactSO, title={Exact sequences on Powell–Sabin splits}, author={Johnny Guzm{\'a}n and Anna Lischke and Michael Neilan}, journal={arXiv: Numerical Analysis}, year={2019} }

We construct smooth finite elements spaces on Powell-Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical $C^1$ Powell-Sabin space, while the others form stable and divergence-free yielding pairs for the Stokes problem. We develop degrees of freedom for these spaces that induce projections that commute with the differential operators.

#### 6 Citations

The Scott-Vogelius Method for Stokes Problem on Anisotropic Meshes

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- ArXiv
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This paper analyzes the Scott-Vogelius divergence-free element pair on anisotropic meshes. We explore the behavior of the inf-sup stability constant with respect to the aspect ratio on meshes… Expand

Nonconforming finite element Stokes complexes in three dimensions

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By the nonconforming finite element Stokes complexes, the mixed finite element methods of the quad-curl problem is decoupled into two mixed method of the Maxwell equation and thenonconforming $P_1$-$P_0$ element method for the Stokes equation, based on which a fast solver is developed. Expand

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This work proves pressure-independent error estimates in the linearized case, known as Oseen's problem, and proves an $O(h^{k+\frac12})$ error estimate in the $L^2$-norm that is known to be the best that can be expected for this type of problem. Expand

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Finite element approximations of the Maxwell eigenvalue problem in two dimensions are considered and, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements is proved. Expand

Exact sequences on Worsey-Farin Splits

- Computer Science, Mathematics
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Several smooth finite element spaces defined on three--dimensional Worsey--Farin splits are constructed and it is shown the discrete spaces satisfy local exactness properties. Expand

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