Istituto di Matematica Applicata e Tecnologie Informatiche     
Cornetti G., Manzini G. The adjoint discontinuous Galerkin method for scalar conservation laws and systems. Technical report ercim.cnr.ian//1998-1080, 1998.
By using the adjoint problem a numerical scheme for scalar conservation laws and systems is derived. The adjoint problem is proved to be well posed for homogeneous convex flux and to have a physical meaning in the case of the Euler equations. The scheme can be interpreted as a discontinuous Galerkin method with piecewise constant interpolation, and it is shown to be monotone for a class of conservation laws. High order accurate solutions are obtained by using higher degree piecewise polynomial interpolation. Numerical examples validate the theoretical results and show the convergence of the scheme when applied to scalar equations with convex and non-convex flux and to systems of hyperbolic equations arising in fluid dynamics, such as the Shallow Water and the compressible Euler equations.
Subject Discontinuous Galerkin Methods

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