Summary
We provide a full description of the Jacobian to the discontinuous Galerkin discretization of the compressible Euler equations, one of the key ingredients of the adaptive discontinuous Galerkin methods recently developed in [7, 8]. We demonstrate the use of this Jacobian within an implicit solver for the approximation of the (primal) stationary flow problems as well as in the adjoint (dual) problems that occur in the context of a posteriori error estimation and adaptive mesh refinement. In particular, we show that the (stationary) compressible Euler equations can efficiently be solved by the Newton method. Full quadratic Newton convergence is achieved on higher order elements as well as on locally refined meshes.
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Hartmann, R. (2005). The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations. In: Warnecke, G. (eds) Analysis and Numerics for Conservation Laws. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-27907-5_13
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DOI: https://doi.org/10.1007/3-540-27907-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24834-7
Online ISBN: 978-3-540-27907-5
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