Abstract: An upwind technique is usually used in order to capture the shocks in the (Jalerkm full potential finite element method for calculating supercritical transonic flows. But it leads to the vibration of the equation of mass conservation. The present formulation extends the Galerkin finite element method by modifying it with penalty function to enforce the conservation of mass across the element interfaces, while allowing sudden changes in velocities and densities in 2-D transonic flows over airfoils. The algorithm is then extended to over three-dimentional wings.

Key words: supercritical transonic flows, Galerkin finite element method, full potential equation