Interior maximum norm estimates for finite element discretizations of the Stokes equations
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. © 2007, Taylor & Francis Group, LLC.
International Journal of Phytoremediation
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Narasimhan, R. and Babuška, I., "Interior maximum norm estimates for finite element discretizations of the Stokes equations" (2007). Kean Publications. 2540.