Abstract
The expanding interest in finite element discrete approximation techniques applied to high speed flow prediction has engendered derivation of many distinct theoretical statements. Quantization of algorithm robustness has focused on accuracy assessment for non-smooth solutions, i.e., those containing shocks and/or contact discontinuities, to reduced forms of the Navier-Stokes equations, specifically the Euler equation system and the transonic potential flow equation. This paper presents derivation of a penalty finite element algorithm applicable to both problem statements, with penalty functional derived as a reduced form of a Taylor-Galerkin weak-statement. Numerical results for shocked transonic and Euler solutions are cited to document aspects of accuracy, convergence and stability.
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