Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for th...

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Veröffentlicht in:Numerical methods for partial differential equations 2017-03, Vol.33 (2), p.489-513
Hauptverfasser: Girault, Vivette, Li, Jizhou, Rivière, Beatrice M.
Format: Artikel
Sprache:eng
Schlagworte:
compactness
Concentration gradient
Convergence
Discontinuity
Galerkin methods
Mathematical analysis
Mathematical models
Mathematics
nonlinear PDEs
Norms
Porous media
weighted Sobolev spaces
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Zusammenfassung:Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the L2 norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22092