A note on a discrete form of Friedrichs’ inequality. (English) Zbl 0537.65073

Čermák, Libor

Apl. Mat. 28, 457-466 (1983).

The main result is a discrete form of Friedrichs’ inequality: \[ \| v\|_{1,\Omega_ h}\leq c(\| v\|_{0,\Gamma^*_ h}+| v|_{1,\Omega_ h}),\quad v\in V_ h. \] Here, \(V_ h\) is a finite element space with simplicial isoparametric elements and a 1- regular triangulation. Inequalities of this type were introduced by A. Ženišek [RAIRO, Anal. Numér. 15, 265-286 (1981; Zbl 0475.65072)] for \(n=2\). In this paper, n-dimensional domains with arbitrary \(n\geq 2\) are treated.

Reviewer: D.Braess

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

finite element method; simplicial isoparametric elements; Friedrichs’ inequality

Citations:

Zbl 0475.65072

References:

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[2]	L. Čermák: The finite element solution of second order elliptic problems with the Newton boundary condition. Apl. Mat., 28 (1983), 430-456. · Zbl 0542.65063
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