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).


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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