Conforming and divergence-free Stokes elements on general triangular meshes
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- by Johnny Guzmán and Michael Neilan PDF
- Math. Comp. 83 (2014), 15-36 Request permission
Abstract:
We present a family of conforming finite elements for the Stokes problem on general triangular meshes in two dimensions. The lowest order case consists of enriched piecewise linear polynomials for the velocity and piecewise constant polynomials for the pressure. We show that the elements satisfy the inf-sup condition and converges with order $k$ for both the velocity and pressure. Moreover, the pressure space is exactly the divergence of the corresponding space for the velocity. Therefore the discretely divergence-free functions are divergence-free pointwise. We also show how the proposed elements are related to a class of $C^1$ elements through the use of a discrete de Rham complex.References
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Additional Information
- Johnny Guzmán
- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
- MR Author ID: 775211
- Email: johnnyguzman@brown.edu
- Michael Neilan
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 824091
- Email: neilan@pitt.edu
- Received by editor(s): October 3, 2011
- Received by editor(s) in revised form: March 29, 2012
- Published electronically: July 25, 2013
- Additional Notes: The first author was supported by the National Science Foundation through grant number DMS-0914596
The second author was supported by the National Science Foundation through grant number DMS-1115421 - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 15-36
- MSC (2010): Primary 76M10, 65N30, 65N12
- DOI: https://doi.org/10.1090/S0025-5718-2013-02753-6
- MathSciNet review: 3120580