| Speaker: | Vivette Girault Chalmers University of Technology |
| Title: | Maximum-norm estimates for finite-element discretizations of the Stokes problem |
We prove stability of the finite element Stokes projection in the product space W^{1,infinity}(Omega)*L^{infinity}(Omega), i.e., the maximum norm of the discrete velocity gradient and discrete pressure are bounded by the sum of the corresponding exact counterparts, independently of the mesh-size. The proof relies on weighted L^2 estimates for regularized Green's functions associated with the Stokes problem and on a weighted inf-sup condition. The domain is a Lipschitz polygon or polyhedron, satisfying suitable sufficient conditions on the inner angles of its boundary, so that the exact solution is bounded in W^{1,infinity}(Omega)*L^{infinity}(Omega). The triangulation is shape-regular and quasi-uniform. The finite element spaces satisfy a super-approximation property, which is shown to be valid for commonly used stable finite delment spaces.
Numerical Analysis
Seminars
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