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On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Eymard, Robert Herbin, Raphaèle Latché, Jean-Claude Piar, Bruno |
| Copyright Year | 2007 |
| Abstract | In this paper, we give a new (and simpler) stability proof for a cell-centered colocated finite volume scheme for the 2D Stokes problem, which may be seen as a particular case of a wider class of methods analyzed in [10]. The definition of this scheme involves two grids. The coarsest is a triangulation of the computational domain by acute-angled simplices, called clusters. The control volumes grid is finer, built by cutting each cluster along the lines joining the mid-edge points to obtain four sub-triangles. By building a Fortin projection operator explicitly, we prove that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is inf-sup stable. In a second step, we prove that a stabilization which involves pressure jumps only across the internal edges of the clusters yields a stable scheme with the usual colocated discretization (i.e., with the cell-centered approximation for the velocity and the pressure). Lastly we give an interpretation of this stabilization as a “minimal stabilization procedure”, as introduced by Brezzi and Fortin.Keywords: Incompressible Stokes equations, Finite volumes, Stability |
| Starting Page | 219 |
| Ending Page | 234 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10092-007-0138-8 |
| Volume Number | 44 |
| Alternate Webpage(s) | https://hal.archives-ouvertes.fr/hal-00136127/document |
| Alternate Webpage(s) | https://doi.org/10.1007/s10092-007-0138-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
