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A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible Euler and Navier-Stokes equations. (English) Zbl 0727.73072

In this paper, we propose a generalization of the element residual method (ERM) to symmetrizable problems which includes such problems of interest as the time-step-dependent boundary value problems resulting from the time discretization of the Euler or Navier-Stokes equations. The natural norm is then identified as the linearized entropy corresponding to a particular solution vector (steady state solution for steady state problems).

MSC:

74S05 Finite element methods applied to problems in solid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
65N15 Error bounds for boundary value problems involving PDEs
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