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Adjoint consistency analysis of discontinuous Galerkin discretizations. (English) Zbl 1189.76341
This paper provides a general unified framework for analyzing the adjoint consistency of discontinuous Galerkin (DG) discretizations which is also useful for the derivation of adjoint consistent methods. This analysis is performed for DG discretizations of linear advection equation, for the interior penalty DG method for elliptic problems (Poisson), and for the DG discretization of compressible Euler equations. This framework is then used to derive an adjoint consistent DG discretization of compressible Navier-Stokes equations. Numerical experiments demonstrate the link of adjoint consistency to the accuracy of numerical flow solutions and to the smoothness of discrete adjoint solutions.

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics, general
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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