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Feedback Petrov-Galerkin methods for convection-dominated problems. (English) Zbl 0753.76093
Summary: The Petrov-Galerkin method introduced in [ibid. 68, No. 1, 83-95 (1988; Zbl 0626.76091)] is adaptively applied to convection-dominated problems. To this end a feedback function is created which increases or decreases the control of the gradient of the approximate solution. This leads to a method with good stability properties close to boundary layers and high accuracy where regular solutions do occur.

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
Full Text: DOI
[1] Brooks, A.N.; Hughes, T.J.R., Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[2] Hughes, T.J.R.; Mallet, M.; Mizukami, A., A new finite element formulation for computational fluid dynamics: II. beyond SUPG, Comput. methods appl. mech. engrg., 54, 341-355, (1986) · Zbl 0622.76074
[3] do Carmo, E.G.; Galeão, A.C., A consistent formulation of the finite element to solve convective-diffuse transport problems, Rev. brasileira cienc. mec., 4, 309-340, (1986), (in Portuguese)
[4] Galeão, A.C.; Dutra do Carmo, E.G., A consistent approximate upwind Petrov-Galerkin formulation for convection-dominated problems, Comput. methods appl. mech. engrg., 68, 83-95, (1988) · Zbl 0626.76091
[5] Johnson, C.; Nävert, U.; Pitkäranta, J., Finite element methods for linear hyperbolic problems, Comput. methods appl. mech. engrg., 45, 285-312, (1984) · Zbl 0526.76087
[6] Dutra do Carmo, E.G.; Galeão, A.C., High order P-G finite elements for convection-dominated problems, (), 151-156
[7] Mizukami, A.; Hughes, T.J.R., A Petrov-Galerkin finite element method for convection-dominated flows: an accurate upwind technique for satisfying the maximum principle, Comput. methods appl. mech. engrg., 50, 181-193, (1985) · Zbl 0553.76075
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