One‐dimensional finite element method in hydrodynamic stability

The stability of plane Poiseuille flow and circular Couette flow are examined with respect to linear azimuthally periodic disturbances by the finite element method. In the case of Couette motion, solutions are obtained for a narrow gap, a wide gap and a dilute polymer solution with an elongational viscosity in the narrow gap limit when both cylinders rotate at almost equal speed in the same direction. Results are in good agreement with previous calculations by other numerical methods.