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We give a derivation for the value of inf-sup constant for the bilinear form(p, div u). We prove that the value of inf-sup constant is equal to 1.0 in allcases and is independent of the size and shape of the domain. Numerical testsfor validation of inf-sup constants is performed using finite dimensionalspaces defined in \cite{2020jain} on two test domains i) a square of size$\Omega = [0,1]^2$, ii) a square of size $\Omega = [0,2]^2$, for varying meshsizes and polynomial degrees. The numeric values are in agreement with thetheoretical value of inf-sup term.

Estimation and numerical validation of inf-sup constant for bilinear form (p, div u)