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- W3149403885 abstract "Let $$Omega $$ be a Lipschitz polyhedral (can be nonconvex) domain in $${mathbb {R}}^{3}$$ , and $$V_{h}$$ denotes the finite element space of continuous piecewise linear polynomials. On non-obtuse quasi-uniform tetrahedral meshes, we prove that the finite element projection $$R_{h}u$$ of $$u in H^{1}(Omega ) cap C({overline{Omega }})$$ (with $$R_{h} u$$ interpolating u at the boundary nodes) satisfies $$begin{aligned} Vert R_{h} uVert _{L^{infty }(Omega )} le C vert log h vert Vert uVert _{L^{infty }(Omega )}. end{aligned}$$ If we further assume $$u in W^{1,infty }(Omega )$$ , then $$begin{aligned} Vert R_{h} uVert _{W^{1, infty }(Omega )} le C vert log h vert Vert uVert _{W^{1, infty }(Omega )}. end{aligned}$$" @default.
- W3149403885 created "2021-04-13" @default.
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- W3149403885 date "2021-04-03" @default.
- W3149403885 modified "2023-10-14" @default.
- W3149403885 title "The Pointwise Stabilities of Piecewise Linear Finite Element Method on Non-obtuse Tetrahedral Meshes of Nonconvex Polyhedra" @default.
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- W3149403885 doi "https://doi.org/10.1007/s10915-021-01465-4" @default.
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