The Pointwise Stabilities of Piecewise Linear Finite Element Method on Non-obtuse Tetrahedral Meshes of Nonconvex Polyhedra

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Original languageEnglish
Article number53
Journal / PublicationJournal of Scientific Computing
Issue number2
Online published3 Apr 2021
Publication statusPublished - May 2021


Let Ω be a Lipschitz polyhedral (can be nonconvex) domain in R3, and Vh denotes the finite element space of continuous piecewise linear polynomials. On non-obtuse quasi-uniform tetrahedral meshes, we prove that the finite element projection Rhu of H1(Ω) ∩ (Ω¯) (with Rhu interpolating u at the boundary nodes) satisfies
RhuL(Ω)C| log |‖uL(Ω).
If we further assume uW1,(Ω), then
RhuW1,∞(Ω)C| log |‖uW1,∞(Ω).

Research Area(s)

  • Finite element method, Nonconvex polyhedra, The stability in L∞ and W1,∞