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Max-Norm Stability of Low Order Taylor–Hood Elements in Three Dimensions

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Abstract

We prove stability in \(W^{1,\infty }(\Omega )\) and \(L^\infty (\Omega )\) for the velocity and pressure approximations, respectively, using the lowest-order Taylor–Hood finite element spaces to solve the three dimensional Stokes problem. The domain \(\Omega \) is assumed to be a convex polyhedra.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Johnny Guzmán & Manuel A. Sánchez

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  1. Johnny Guzmán
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  2. Manuel A. Sánchez
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Correspondence to Manuel A. Sánchez.

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Guzmán, J., Sánchez, M.A. Max-Norm Stability of Low Order Taylor–Hood Elements in Three Dimensions. J Sci Comput 65, 598–621 (2015). https://doi.org/10.1007/s10915-014-9978-y

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  • DOI: https://doi.org/10.1007/s10915-014-9978-y

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