Discrete Friedrich's and Korn's inequalities. I (Q2721770)

In the finite element method it is often necessary to replace the original domain \(\Omega\) by computational domains \(\Omega_h\) arizing from the finite element triangulation where the computational domains \(\Omega_h\) approximate \(\Omega\) if the discretization parameter \(h\) tends to \(0\). The author proves discrete (i.e. living on \(\Omega_h\) instead of \(\Omega\)) counterparts of Friedrichs-like and Korn-like inequalities with positive constants that are uniformly bounded with respect to the discretization parameter \(h\). These inequalities are needed in the numerical analysis of the corresponding finite element schemes.