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Oden, J. T.; Demkowicz, L.; Rachowicz, W.; Westermann, T. A.

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

Comput. Methods Appl. Mech. Eng. 82, No. 1-3, 183-203 (1990).
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).

Cited in 22 Documents

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

Keywords:

time-step-dependent boundary value problems; time discretization; natural norm; linearized entropy
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\textit{J. T. Oden} et al., Comput. Methods Appl. Mech. Eng. 82, No. 1--3, 183--203 (1990; Zbl 0727.73072)
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References:

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