An adaptive Petrov-Galerkin formulation for the compressible Euler and Navier-Stokes equations

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In this paper we combine a stable Petrov-Galerkin formulation for the compressible Euler and Navier-Stokes equations with an h-adaptive remeshing refinement, including directional stretching and stretching ratio in the mesh regeneration procedure. The result is an accurate and efficient scheme appropriated to solve problems presenting shocks and boundary-layers.