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Analysis of the finite element variational crimes in the numerical approximation of transonic flow. (English) Zbl 0786.76051
A convergence analysis of a piecewise linear finite element method for transonic potential flow is given. The full potential equation is considered in a bounded domain with mixed Dirichlet-Neumann boundary conditions. A new version of entropy compactification of transonic flow and the theory of variational crimes enable the authors to develop a detailed theory of a conforming piecewise linear FEM in which the occuring integrals are treated by means of quadrature rules. In the convergence proof of the authors assume the existence of a solution of the physical problem.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76H05 Transonic flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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