nach oben

Journal of Scientific Computing

Erschienen in:

07.03.2017

A Mortar Mixed Finite Volume Method for Elliptic Problems on Non-matching Multi-block Triangular Grids

verfasst von: Yanni Gao, Yonghai Li

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

A mixed finite volume method is considered for the mixed formulation of second-order elliptic equations. The computational domain can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domain independently, and employ the standard mixed finite volume method within each sub-domain. A mortar finite element space is introduced to approximate the trace of the pressure on the non-matching interfaces. Moreover, a continuity condition of flux is imposed weakly. We prove the scheme’s first order optimal rate of convergence for both the pressure and the velocity. Numerical experiments are provided to illustrate the error behavior of the scheme and confirm our theoretical results.

Vorheriger Artikel The Time Second Order Mass Conservative Characteristic FDM for Advection–Diffusion Equations in High Dimensions

Nächster Artikel A Block-Centered Finite Difference Method for Slightly Compressible Darcy–Forchheimer Flow in Porous Media

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Arbogast, T., Cowsar, L.C., Wheeler, M.F., Yotov, I.: Mixed finite element methods on non-matching multiblock grids. SIAM J. Numer. Anal. 37, 1295–1315 (2000)MathSciNetCrossRefMATH

Arbogast, T., Xiao, H.L.: Two-level mortar domain decomposition preconditioners for heterogeneous elliptic problems. Comput. Methods Appl. Mech. Eng. 292, 221–242 (2015)MathSciNetCrossRef

Arbogast, T., Yotov, I.: A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids. Comput. Methods Appl. Mech. Eng. 149, 255–265 (1997)MathSciNetCrossRefMATH

Bi, C.J.: Superconvergence of mixed covolume method for elliptic problems on triangular grids. J. Comput. Appl. Math. 216, 534–544 (2008)MathSciNetCrossRefMATH

Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)CrossRefMATH

Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, 3rd edn. Springer, New York (2008)

Cai, Z.Q.: On the finite volume element method. Numer. Math. 58, 713–735 (1991)MathSciNetCrossRefMATH

Chou, S.H., Kwak, D.Y.: Mixed covolume methods on rectangular grids for elliptic problems. SIAM J. Numer. Anal. 37, 758–771 (2000)MathSciNetCrossRefMATH

Chou, S.H., Kwak, D.Y., Kim, K.Y.: A general framework for constructing and analyzing mixed finite volume methods on quadrilateral grids: the overlapping covolume case. SIAM J. Numer. Anal. 39, 1170–1196 (2001)MathSciNetCrossRefMATH

10.

Chou, S.H., Kwak, D.Y., Kim, K.Y.: Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems. Math. Comput. 72, 525–539 (2003)MathSciNetCrossRefMATH

11.

Chou, S.H., Kwak, D.Y., Vassilevski, P.S.: Mixed covolume methods for elliptic problems on triangular grids. SIAM J. Numer. Anal. 35, 1850–1861 (1998)MathSciNetCrossRefMATH

12.

Chou, S.H., Li, Q.: Error estimates in \(L^2\), \(H^1\), \(L^\infty \) in covolume methods for elliptic and parabolic problem: a unified approach. Math. Comput. 69, 103–120 (2000)MathSciNetCrossRefMATH

13.

Ciarlet, P.G., Raviart, P.A., Lions, J.L.: General lagrange and hermite interpolation in \({\mathbb{R}}^n\) with alpplications to finite element methods. Arch. Ration. Mech. Anal. 46, 177–199 (1972)CrossRefMATH

14.

Chen, Z.Y., Xu, Y.S., Zhang, Y.Y.: A construction of highter-order finite volume methods. Math. Comput. 84(292), 599–628 (2014)CrossRef

15.

Ganis, B., Wheeler, M.F., Yotov, I.: An enhanced velocity multipoint flux mixed finite element method for Darcy flow on non-matching hexahedral grids. Proced. Comput. Sci. 51, 1198–1207 (2015)CrossRef

16.

Girault, V., Vassilev, D., Yotov, I.: Mortar multiscale finite element methods for Stokes–Darcy flows. Numer. Math. 127, 93–165 (2014)MathSciNetCrossRefMATH

17.

Li, R.H., Chen, Z.Y., Wu, W.: Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods. Marcel Dekker, New York (2000)MATH

18.

Lv, J.L., Li, Y.H.: Optimal biquadratic finite volume element methods on quadrilateral meshes. SIAM J. Numer. Anal. 50, 2379–2399 (2012)MathSciNetCrossRefMATH

19.

Mishev, I.D.: Analysis of a new mixed finite volume method. Comput. Methods Appl. Math. 3, 189–201 (2003)MathSciNetCrossRefMATH

20.

Pan, H., Rui, H.X.: Mixed element method for two-dimensional Darcy–Forchheimer model. J. Sci. Comput. 52, 563–587 (2012)MathSciNetCrossRefMATH

21.

Rui, H.X.: Superconvergence of a mixed covolume method for elliptic problems. Computing 71, 247–263 (2003)MathSciNetCrossRefMATH

22.

Rui, H.X.: Convergence of an upwind control-volume mixed finite element method for convection-diffusion problems. Computing 81, 297–315 (2007)MathSciNetCrossRefMATH

23.

Rui, H.X., Lu, T.C.: An expanded mixed covolume method for elliptic problems. Numer. Methods Partial Differ. Equ. 21, 8–23 (2005)MathSciNetCrossRefMATH

24.

Rui, H.X., Zhang, R.: A unified stabilized mixed finite element method for coupling Stokes and Darcy flows. Comput. Methods Appl. Mech. Eng. 198, 2692–2699 (2009)MathSciNetCrossRefMATH

25.

Thomas, S.G., Wheeler, M.F.: Enhanced velocity mixed finite element methods for modeling coupled flow and transport on non-matching multiblock grids. Comput. Geosci. 15, 605–625 (2011)MathSciNetCrossRefMATH

26.

Tian, W.F., Li, Y.H.: Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems. J. Syst. Sci. Complex. 25, 385–397 (2012)MathSciNetCrossRefMATH

27.

Tian, W.F., Song, L.Q., Li, Y.H.: A stabilized equal-order finite volume method for the stokes equations. J. Comput. Math. 30, 615–628 (2012)MathSciNetCrossRefMATH

28.

Tunc, X., Faille, I., Gallouët, T., Cacas, M.C., Havé, P.: A model for conductive faults with non-matching grids. Comput. Geosci. 16, 277–296 (2012)CrossRefMATH

29.

Vassilev, D., Wang, C.Q., Yotov, I.: Domain decomposition for coupled Stokes and Darcy flows. Comput. Methods Appl. Mech. Eng. 268, 264–283 (2014)MathSciNetCrossRefMATH

30.

Wheeler, J.A., Wheeler, M.F., Yotov, I.: Enhanced velocity mixed finite element methods for flow in multiblock domains. Comput. Geosci. 6, 315–332 (2002)MathSciNetCrossRefMATH

31.

Yotov, I.: Mixed finite element methods for flow in porous media, Ph.D. Thesis, Rice University, Houston (1996)

32.

Zhao, X.K., Chen, Y.L., Lv, J.L.: A mixed nonoverlapping covolume method on quadrilateral grids for elliptic problems. J. Comput. Appl. Math. 292, 23–40 (2016)MathSciNetCrossRefMATH

33.

Zhang, Z.M., Zou, Q.S.: Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems. Numer. Math. 130, 363–393 (2015)MathSciNetCrossRefMATH

Titel: A Mortar Mixed Finite Volume Method for Elliptic Problems on Non-matching Multi-block Triangular Grids
verfasst von: Yanni Gao
Yonghai Li
Publikationsdatum: 07.03.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0405-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2017

Spectral Method for Vorticity-Stream Function Form of Navier–Stokes Equations in an Infinite Channel with Slip Boundary Conditions

A Block-Centered Finite Difference Method for Slightly Compressible Darcy–Forchheimer Flow in Porous Media

An Efficient Energy Minimization for Conformal Parameterizations

The Time Second Order Mass Conservative Characteristic FDM for Advection–Diffusion Equations in High Dimensions

Tailored Finite Point Methods for Solving Singularly Perturbed Eigenvalue Problems with Higher Eigenvalues

Convergence and Quasi-Optimality of an Adaptive Finite Element Method for Optimal Control Problems on Errors