Dana Ríhová-Skabrahová

Address. Technical University Brno, Faculty of Technology - Department of Mathematics, Mostn¡ 5139, 762 72 Zl¡n, CZECH REPUBLIC

E-mail: skabrahova@zlin.vutbr.cz

Abstract. The main aim of this paper is to derive continuous and discrete forms of inequalities which are similar to Friedrichs' inequality and to show that for $h$ sufficiently small the constant $C$ appearing in discrete inequalities written for functions from finite element spaces $X_h$ is independent of $h$. The discrete forms of Friedrichs' inequality are restricted to two-dimensional domains in this paper. These inequalities have applications in the theory of two-dimensional electromagnetic field and in the analysis of the approximate solution of Maxwell's equations.

AMSclassification. 65N30

Keywords. Finite element method, two-dimensional electromagnetic field, Friedrichs' inequality, discrete forms of Friedrichs' inequality