The Pointwise Stabilities of Piecewise Linear Finite Element Method on Non-obtuse Tetrahedral Meshes of Nonconvex Polyhedra
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 53 |
Journal / Publication | Journal of Scientific Computing |
Volume | 87 |
Issue number | 2 |
Online published | 3 Apr 2021 |
Publication status | Published - May 2021 |
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Abstract
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 u ∈ H1(Ω) ∩ C (Ω¯) (with Rhu interpolating u at the boundary nodes) satisfies
‖Rhu‖L∞(Ω) ≤ C| log h |‖u‖L∞(Ω).
If we further assume u ∈ W1,∞(Ω), then
‖Rhu‖W1,∞(Ω) ≤ C| log h |‖u‖W1,∞(Ω).
‖Rhu‖L∞(Ω) ≤ C| log h |‖u‖L∞(Ω).
If we further assume u ∈ W1,∞(Ω), then
‖Rhu‖W1,∞(Ω) ≤ C| log h |‖u‖W1,∞(Ω).
Research Area(s)
- Finite element method, Nonconvex polyhedra, The stability in L∞ and W1,∞
Citation Format(s)
The Pointwise Stabilities of Piecewise Linear Finite Element Method on Non-obtuse Tetrahedral Meshes of Nonconvex Polyhedra. / Gao, Huadong; Qiu, Weifeng.
In: Journal of Scientific Computing, Vol. 87, No. 2, 53, 05.2021.
In: Journal of Scientific Computing, Vol. 87, No. 2, 53, 05.2021.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review