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An adaptive finite element method for inviscid compressible flow. (English) Zbl 1427.76139

Summary: We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
35Q31 Euler equations
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