A stabilized finite element method based on two local Gauss integrations for the Stokes equations
By Jian Li, Yinnian He. 2008
238 citations recorded by the source corpus.
This paper considers a stabilized method based on the difference between a consistent and an under-integrated mass matrix of the pressure for the Stokes equations approximated by the lowest equal-order finite element pairs (i.e., the P"1-P"1 and Q"1-Q"1 pairs). This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. Optimal error estimates are obtained by applying the standard Galerkin technique. Finally, the numerical illustrations agree completely with the theoretical expectations.
Subfields: Computational Mechanics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/0ce26c7cb783b8a45a69ed124605da40dc67be9f
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In Computational Mechanics
- Peter Hansbo
- Roland Becker
- Erik Burman
- John Dolbow
- Paul Houston
- Ted Belytschko
- Anna Scotti
- Dominik Schillinger
In Numerical Analysis
Citations in the corpus
- A simple pressure stabilization method for the Stokes equation (2007, methodology): “This allows for a direct analogy with the method of Dohrmann and Bochev [7]; indeed the methods of [7, 9] are identical from a numerical point of view for these low-order approximations.”
- Characteristic stabilized finite element method for the transient Navier–Stokes equations (2010, unknown): “Let (Xh,Mh) be defined as above [32].”