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 \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 mesh sizes and polynomial degrees. The numeric values are in agreement with the theoretical value of inf-sup term.
翻译：我们给出了双线形(p, div u) Inf-sup常量值的推算。 我们证明, Inf-sup常量值在所有情况下均等于 1.0, 与域的大小和形状无关。 用于校验 inf-sup常量的数值测试使用两个测试域i 中\ cite{2020jain} 定义的有限维空间进行。 一个面积为$\ Omega = [0, 1, ⁇ 2$, ii) 一个面积为$\ Omega = [0, 2] 的平方, 用于不同的网状大小和多面度。 数字值与 Inf-sup 术语的理论值一致。
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