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Register a new userEstimation and numerical validation of inf-sup constant for bilinear form (p, div u)
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Added by
Varun Jain
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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 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.
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This paper is in relation with a Note of Comptes Rendus de lAcademie des Sciences 2005. We have an idea about a lower bounds of sup+inf (2 dimensions) and sup*inf (dimensions >2).
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