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

Johnny Guzmán; Manuel A. Sánchez

doi:10.1007/s10915-014-9978-y

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

Johnny Guzmán, Manuel A. Sánchez

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove stability in W^1,∞(Ω) and L^∞(Ω) 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 Ω is assumed to be a convex polyhedra.

Original language	English (US)
Pages (from-to)	598-621
Number of pages	24
Journal	Journal of Scientific Computing
Volume	65
Issue number	2
DOIs	https://doi.org/10.1007/s10915-014-9978-y
State	Published - Nov 1 2015

Keywords

Finite element
Maximum norm
Optimal error estimates
Stokes

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10.1007/s10915-014-9978-y

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abstract = "We prove stability in W1,∞(Ω) and L∞(Ω) 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 Ω is assumed to be a convex polyhedra.",

keywords = "Finite element, Maximum norm, Optimal error estimates, Stokes",

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T1 - Max-Norm Stability of Low Order Taylor–Hood Elements in Three Dimensions

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AU - Sánchez, Manuel A.

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N2 - We prove stability in W1,∞(Ω) and L∞(Ω) 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 Ω is assumed to be a convex polyhedra.

AB - We prove stability in W1,∞(Ω) and L∞(Ω) 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 Ω is assumed to be a convex polyhedra.

KW - Finite element

KW - Maximum norm

KW - Optimal error estimates

KW - Stokes

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

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