Finite element analysis of the stability of fluid motions (Q1107386)

The linear and global theories of stability of buoyancy-driven flows are reviewed, and corresponding eigenvalue problems whose eigenvalues give critical values of Rayleigh number are formulated in variational form. Penalty-finite element approximations of these problems are constructed. After a discussion of the properties of the solutions, the formulation is applied to the problem of stability of a container of fluid containing internal heat sources and heated from below.