On the inf-sup condition of mixed finite element formulations for acousticfluids

The objective of this paper is to present a study of the solvability, stabi lity and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is giv en, and the interrelationship between the inf-sup condition, including the numerical inf-sup test, and the eigenvalue problem pertaining to the natura l frequencies is discussed.