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

05/22/2021

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by   V. Jain, et al.

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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 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 <cit.> 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.