  The paper is concerned with sharp estimates of constants in Poincare type
inequalities for functions having zero mean value on the boundary of a
Lipschitz domain or on a measurable part of it. These estimates are useful for
various numerical methods, in particular, for a posteriori error estimation
methods for partial differential equations (PDEs). Therefore, we are mainly
focused on domains typical for numerical analysis (simplexes in 2d and 3d) and
suggest easily computable relations that provide sharp bounds of the respective
constants. Also, we investigate numerically the behavior of the constants in
the classical Poincare inequalities and compare these results with known
analytical estimates. In the last section, the estimates are used in order to
obtain new a posteriori estimates for an elliptic boundary value problem.
