A convergent finite element formulation for transonic flow

Summary A finite element formulation for the full potential equation in the case of two-dimensional transonic flow is presented. The formulation is based on an optimal control approach developed by Glowinski and Pironneau. The solution of the full potential equation is obtained by a minimization problem. Using a new compactness result it is possible to prove convergence for the solutions of the minimization problem. The a priori assumption of existence and uniqueness of a weak solution of the full potential equation satisfying an entropy condition implies that the limit function must be the solution. It is possible to extend the convergence result to the case of three-dimensional transonic potential flow.The research reported here was supported by a grant from the Stiftung Volkswagenwerk, Federal Republic of Germany. It is a part of the doctoral thesis of the above author, Universität Stuttgart 1989