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