Abstract
Interior estimates are proved in the L ∞ norm for stable finite element discretizations of the Stokes equations on translation invariant meshes. These estimates yield information about the quality of the finite element solution in subdomains a positive distance from the boundary. While they have been established for second-order elliptic problems, these interior, or local, maximum norm estimates for the Stokes equations are new. By applying finite differenciation methods on a translation invariant mesh, we obtain optimal convergence rates in the mesh size h in the maximum norm. These results can be used for analyzing superconvergence in finite element methods for the Stokes equations.
Original language | English |
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Pages (from-to) | 251-260 |
Number of pages | 10 |
Journal | International Journal of Phytoremediation |
Volume | 86 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2007 |
Keywords
- 2000 Mathematics Subject Classifications: Primary: 65N15
- Interior error estimates
- Mixed finite element method
- Secondary: 65N30
- Stokes equations