ANALYSIS OF THE FINITE-ELEMENT VARIATIONAL CRIMES IN THE NUMERICAL APPROXIMATION OF TRANSONIC FLOW

The paper presents a detailed theory of the finite element approximati ons of two-dimensional transonic potential flow. We consider the bound ary value problem for the full potential equation in a general bounded domain OMEGA with mixed Dirichlet-Neumann boundary conditions. In the discretization of the problem we proceed as usual in practice: the do main OMEGA is approximated by a polygonal domain, conforming piecewise linear triangular elements are used, and the integrals are evaluated by numerical quadratures. Using a new version of entropy compactificat ion of transonic flow and the theory of finite element variational cri mes for nonlinear elliptic problems, we prove the convergence of appro ximate solutions to the exact physical solution of the continuous prob lem, provided its existence can be shown.