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The paper is concerned with sharp estimates of constants in Poincare typeinequalities for functions having zero mean value on the boundary of aLipschitz domain or on a measurable part of it. These estimates are useful forvarious numerical methods, in particular, for a posteriori error estimationmethods for partial differential equations (PDEs). Therefore, we are mainlyfocused on domains typical for numerical analysis (simplexes in 2d and 3d) andsuggest easily computable relations that provide sharp bounds of the respectiveconstants. Also, we investigate numerically the behavior of the constants inthe classical Poincare inequalities and compare these results with knownanalytical estimates. In the last section, the estimates are used in order toobtain new a posteriori estimates for an elliptic boundary value problem.

Sharp bounds of constants in Poincare type inequalities for polygonal domains