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Residual based error estimates for the space-time discontinuous Galerkin method applied to the compressible flows. (English) Zbl 1390.76307

Summary: We develop an adaptive numerical method for solution of the non-stationary compressible Navier-Stokes equations. This method is based on the space-time discontinuous Galerkin discretization, which employs high polynomial approximation degrees with respect to the space as well as to the time coordinates. We focus on the identification of the computational errors, following from the space and time discretizations and from the inexact solution of the arising nonlinear algebraic systems. We derive the residual-based error estimates approximating these errors. Then we propose an efficient algorithm which brings the algebraic, spatial and temporal errors under control. The computational performance of the proposed method is demonstrated by numerical experiments.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76Nxx Compressible fluids and gas dynamics

Software:

ANGENER; RODAS
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