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An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this(More)
In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier–Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical(More)
Meeting. AIAA, AFOSR and DLR provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are(More)
In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier– Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization(More)
10 In this work we extend the high-order Discontinuous Galerkin (DG) Finite element 11 method to inviscid low Mach number flows. The method here presented is designed 12 to improve the accuracy and efficiency of the solution at low Mach numbers using 13 both explicit and implicit schemes for the temporal discretization of the compress-14 ible Euler(More)
In this article we propose a new symmetric version of the interior penalty dis-continuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest,(More)
Important quantities in aerodynamic flow simulations are the aerodynamic force coefficients including the pressure induced and the viscous stress induced drag, lift and moment coefficients. In addition to the exact approximation of these quantities it is of increasing importance, in particular in the field of uncertainty quantification, to estimate the(More)
The aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems arising from the discontinuous Galerkin method. The smoothed aggregation multigrid, introduced by Vaněk for the conforming finite element method, is applied to low-order discretizations of(More)