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

Abstract

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 all cases and is independent of the size and shape of the domain. Numerical tests for validation of inf-sup constants is performed using finite dimensional spaces defined in [1] on two test domains i) a square of size Ω = [0, 1] 2 , ii) a square of size Ω = [0, 2] 2 , for varying mesh sizes and polynomial degrees. The numeric values are in agreement with the theoretical value of inf-sup term.