On the finite element approach to the stability of superposed fluids

Superposed fluids whether in motion or in stationary state may develop instability conditions at their fluid interfaces for critical values of certain parameters related to the geometric dimensions and to the critical properties of the fluids. The problem is analyzed through linear perturbation theory in the case of the instability of incompressible heavy fluid of variable density. Results known for some related inverse operators are applied to the direct operators after a theoretical proof. A numerical method based on finite element method is applied to the problem studied by direct operators. Numerical results are obtained.