An adjoint consistency analysis for a class of hybrid mixed methods

Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In Schütz and May (2013, AICES Technical Report 2011/12-01. Aachen Institute for Advanced Study in Computational Engineering Science), we have introduced a hybrid mixed method for the compressible Navier-Stokes equations as a combination of a hybridized discontinuous Galerkin (DG) scheme for the convective terms, and an H(div, Ω) method for the diffusive part. Since hybrid methods are based on Galerkin's principle, the adjoint of a given hybrid discretization may be used for PDE-constraint optimal control problems, or error estimation. In this regard it is desirable that the discrete adjoint is a consistent approximation of the continuous adjoint. In the present paper, we extend the adjoint consistency analysis, previously reported for many DG schemes, to the more complex hybrid methods. We prove adjoint consistency for a class of hybrid mixed schemes, which includes the hybridized DG schemes proposed by Nguyen et al. (2009, J. Comput. Phys., 228, 8841-8855), as well as our recently proposed method. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Duke Scholars

Author Georg May DKU Faculty