Abstract
The paper is concerned with sharp estimates of constants in the classical Poincaré inequalities and Poincaré-type inequalities for functions with zero mean values in a simplicial domain or on a part of the boundary. These estimates are important for quantitative analysis of problems generated by differential equations where numerical approximations are typically constructed with the help of simplicial meshes. We suggest easily computable relations that provide sharp bounds of the respective constants and compare these results with analytical estimates (if such estimates are known). In the last section, we discuss possible applications and derive a computable majorant of the difference between the exact solution of a boundary value problem and an arbitrary finite dimensional approximation defined on a simplicial mesh.
Funding source: Suomalainen Tiedeakatemia Foundation
Funding source: RFBR
Award Identifier / Grant number: 14-01-00162/15
© 2016 by De Gruyter
