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Volumn 31, Issue 3, 2011, Pages 786-812

Numerical computation of advection and diffusion on evolving diffuse interfaces

Author keywords

advection diffusion equation; diffuse interfaces; double obstacle; finite element; mean curvature; phase field; surface partial differential equation; surfactant

Indexed keywords

ADVECTION; DIFFUSION; FINITE ELEMENT METHOD; PARTIAL DIFFERENTIAL EQUATIONS; SURFACE ACTIVE AGENTS;

EID: 79960506297     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drq005     Document Type: Article
Times cited : (70)

References (52)
  • 1
    • 79960511136 scopus 로고    scopus 로고
    • Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
    • Leipzig: Max Planck Institute
    • ABELS, H. & R̈OGER, M. (2008) Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. Technical Report 71. Leipzig: Max Planck Institute.
    • (2008) Technical Report 71
    • Abels, H.1    R̈oger, M.2
  • 2
    • 0037429531 scopus 로고    scopus 로고
    • Transport and diffusion of material quantities on propagating interfaces via level set methods
    • DOI 10.1016/S0021-9991(02)00057-8
    • ADALSTEINSSON, D. & SETHIAN, J. A. (2003) Transport and diffusion of material quantities on propagating interfaces via level set methods. J. Comput. Phys., 185, 271-288. (Pubitemid 36270002)
    • (2003) Journal of Computational Physics , vol.185 , Issue.1 , pp. 271-288
    • Adalsteinsson, D.1    Sethian, J.A.2
  • 3
    • 0039419221 scopus 로고
    • A finite element method for solving elliptic equations with Neumann data on a curved boundary using unfitted meshes
    • BARRETT, J. & ELLIOTT, C. M. (1984) A finite element method for solving elliptic equations with Neumann data on a curved boundary using unfitted meshes. IMA J. Numer. Anal., 4, 309-325.
    • (1984) IMA J. Numer. Anal. , vol.4 , pp. 309-325
    • Barrett, J.1    Elliott, C.M.2
  • 4
    • 77950294271 scopus 로고
    • Finite element approximation of elliptic equations with Neumann or Robin condition on a curved boundary
    • BARRETT, J. & ELLIOTT, C. M. (1988) Finite element approximation of elliptic equations with Neumann or Robin condition on a curved boundary. IMA J. Numer. Anal., 8, 321-342.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 321-342
    • Barrett, J.1    Elliott, C.M.2
  • 5
    • 0007425693 scopus 로고    scopus 로고
    • Finite element approximation of the Cahn-Hilliard equation with degenerate mobility
    • BARRETT, J. W., BLOWEY, J. F. & GARCKE, H. (1999) Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. SIAM J. Numer. Anal., 37, 286-318.
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 286-318
    • Barrett, J.W.1    Blowey, J.F.2    Garcke, H.3
  • 6
    • 18444382709 scopus 로고    scopus 로고
    • Finite element approximation of a phase field model for void electromigration
    • DOI 10.1137/S0036142902413421
    • BARRETT, J. W., N̈U RNBERG, R. & STYLES, V. M. (2004) Finite element approximation of a phase field model for void electromigration. SIAM J. Numer. Anal., 42, 738-772. (Pubitemid 40645213)
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.2 , pp. 738-772
    • Barrett, J.W.1    Nurnberg, R.2    Styles, V.3
  • 7
    • 0035842857 scopus 로고    scopus 로고
    • Variational problems and partial differential equations on implicit surfaces
    • BERTALMÍO, M., CHENG, L.-T., OSHER, S. J. & SAPIRO, G. (2001) Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys., 174, 759-780.
    • (2001) J. Comput. Phys. , vol.174 , pp. 759-780
    • Bertalmío, M.1    Cheng, L.-T.2    Osher, S.J.3    Sapiro, G.4
  • 9
    • 84971972596 scopus 로고
    • The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy part i: Mathematical analysis
    • BLOWEY, J. F. & ELLIOTT, C. M. (1991) The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy part i: mathematical analysis. Eur. J. Appl. Math., 2, 233-280.
    • (1991) Eur. J. Appl. Math. , vol.2 , pp. 233-280
    • Blowey, J.F.1    Elliott, C.M.2
  • 10
    • 84972038069 scopus 로고
    • The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy part ii: Numerical analysis
    • BLOWEY, J. F. & ELLIOTT, C. M. (1992) The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy part ii: numerical analysis. Eur. J. Appl. Math., 3, 147-179.
    • (1992) Eur. J. Appl. Math. , vol.3 , pp. 147-179
    • Blowey, J.F.1    Elliott, C.M.2
  • 11
    • 0002252307 scopus 로고
    • Curvature dependent phase boundary motion and parabolic obstacle problems
    • Degenerate Diffusion (W.-M. Ni, L. A. Peletier & J. L. Vasquez eds) New York: Springer
    • BLOWEY, J. F. & ELLIOTT, C. M. (1993) Curvature dependent phase boundary motion and parabolic obstacle problems. Degenerate Diffusion (W.-M. Ni, L. A. Peletier & J. L. Vasquez eds). IMA Volumes in Mathematics and Its Applications, vol. 47. New York: Springer, pp. 19-60.
    • (1993) IMA Volumes in Mathematics and Its Applications , vol.47 , pp. 19-60
    • Blowey, J.F.1    Elliott, C.M.2
  • 12
    • 0036028061 scopus 로고    scopus 로고
    • A theoretical and numerical model for the study of incompressible mixture flows
    • DOI 10.1016/S0045-7930(00)00031-1, PII S0045793000000311, A tribute to Dr Richard Beam and Dr Robert Warming
    • BOYER, F. (2002) A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids, 31, 41-68. (Pubitemid 32919222)
    • (2002) Computers and Fluids , vol.31 , Issue.1 , pp. 41-68
    • Boyer, F.1
  • 13
    • 33646973938 scopus 로고
    • Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations
    • CAGINALP, G. (1989) Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations. Phys. Rev. A, 39, 5887-5896.
    • (1989) Phys. Rev. A , vol.39 , pp. 5887-5896
    • Caginalp, G.1
  • 14
    • 0037849059 scopus 로고
    • Asymptotics for a parabolic double obstacle problem
    • CHEN, X. & ELLIOTT, C. M. (1994) Asymptotics for a parabolic double obstacle problem. Proc. R. Soc. Lond. Ser. A, 444, 429-445.
    • (1994) Proc. R. Soc. Lond. Ser. A , vol.444 , pp. 429-445
    • Chen, X.1    Elliott, C.M.2
  • 15
    • 19844369196 scopus 로고    scopus 로고
    • Computation of geometric partial differential equations and mean curvature flow
    • DOI 10.1017/S0962492904000224
    • DECKELNICK, K., DZIUK, G. & ELLIOTT, C. M. (2005) Computation of geometric partial differential equations and mean curvature flow. Acta Numer., 14, 139-232. (Pubitemid 40763883)
    • (2005) Acta Numerica , vol.14 , pp. 139-232
    • Deckelnick, K.1    Dziuk, G.2    Elliott, C.M.3
  • 16
    • 77950259990 scopus 로고    scopus 로고
    • An h-narrow band finite-element method for elliptic equations on implicit surfaces
    • DECKELNICK, K., DZIUK, G., ELLIOTT, C. M. & HEINE, C.-J. (2010) An h-narrow band finite-element method for elliptic equations on implicit surfaces. IMA J. Numer. Anal., 30, 351-376.
    • (2010) IMA J. Numer. Anal. , vol.30 , pp. 351-376
    • Deckelnick, K.1    Dziuk, G.2    Elliott, C.M.3    Heine, C.-J.4
  • 18
    • 0010974195 scopus 로고
    • Finite elements for the Beltrami operator on arbitrary surfaces
    • Partial Differential Equations and Calculus of Variations (S. Hildebrandt & R. Leis eds) Berlin: Springer
    • DZIUK, G. (1988) Finite elements for the Beltrami operator on arbitrary surfaces. Partial Differential Equations and Calculus of Variations (S. Hildebrandt & R. Leis eds). Lecture Notes in Mathematics, vol. 1357. Berlin: Springer, pp. 142-155.
    • (1988) Lecture Notes in Mathematics , vol.1357 , pp. 142-155
    • Dziuk, G.1
  • 19
    • 34447646892 scopus 로고    scopus 로고
    • Finite elements on evolving surfaces
    • DZIUK, G. & ELLIOTT, C. M. (2007a) Finite elements on evolving surfaces. IMA J. Numer. Anal., 25, 385-407.
    • (2007) IMA J. Numer. Anal. , vol.25 , pp. 385-407
    • Dziuk, G.1    Elliott, C.M.2
  • 20
    • 34447646892 scopus 로고    scopus 로고
    • Surface finite elements for parabolic equations
    • DZIUK, G. & ELLIOTT, C. M. (2007b) Surface finite elements for parabolic equations. J. Comput. Math., 25, 385-407. (Pubitemid 47085773)
    • (2007) Journal of Computational Mathematics , vol.25 , Issue.4 , pp. 385-407
    • Dziuk, G.1    Elliott, C.M.2
  • 21
    • 42449090766 scopus 로고    scopus 로고
    • Eulerian finite element method for parabolic PDEs on implicit surfaces
    • DZIUK, G. & ELLIOTT, C. M. (2008) Eulerian finite element method for parabolic PDEs on implicit surfaces. Interfaces Free Bound., 10, 119-138.
    • (2008) Interfaces Free Bound. , vol.10 , pp. 119-138
    • Dziuk, G.1    Elliott, C.M.2
  • 22
    • 72149102491 scopus 로고    scopus 로고
    • An Eulerian approach to transport and diffusion on evolving implicit surfaces
    • DZIUK, G. & ELLIOTT, C. M. (2010) An Eulerian approach to transport and diffusion on evolving implicit surfaces. Comput. Vis. Sci., 13, 17-28.
    • (2010) Comput. Vis. Sci. , vol.13 , pp. 17-28
    • Dziuk, G.1    Elliott, C.M.2
  • 23
    • 53349164104 scopus 로고    scopus 로고
    • Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method
    • EILKS, C. & ELLIOTT, C. M. (2008) Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. J. Comput. Phys., 227, 9727-9741.
    • (2008) J. Comput. Phys. , vol.227 , pp. 9727-9741
    • Eilks, C.1    Elliott, C.M.2
  • 24
    • 18444402723 scopus 로고
    • One dimensional phase field computations
    • Numerical Analysis 1993 (D. F. Griffiths & G. A. Watson eds) Essex, UK: Longman Scientific and Technical
    • ELLIOTT, C. M. & GARDINER, A. R. (1994) One dimensional phase field computations. Numerical Analysis 1993 (D. F. Griffiths & G. A. Watson eds). Pitman Research Notes in Mathematics Series, vol. 303. Essex, UK: Longman Scientific and Technical, pp. 56-74.
    • (1994) Pitman Research Notes in Mathematics Series , vol.303 , pp. 56-74
    • Elliott, C.M.1    Gardiner, A.R.2
  • 25
    • 67650083559 scopus 로고    scopus 로고
    • Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface
    • ELLIOTT, C. M. & STINNER, B. (2009a) Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Math. Models Methods Appl. Sci., 19, 1-16.
    • (2009) Math. Models Methods Appl. Sci. , vol.19 , pp. 1-16
    • Elliott, C.M.1    Stinner, B.2
  • 28
    • 0038286318 scopus 로고    scopus 로고
    • Computations of bidirectional grain boundary dynamics in thin metallic films
    • ELLIOTT, C. M. & STYLES, V. M. (2003) Computations of bidirectional grain boundary dynamics in thin metallic films. J. Comput. Phys., 187, 524-543.
    • (2003) J. Comput. Phys. , vol.187 , pp. 524-543
    • Elliott, C.M.1    Styles, V.M.2
  • 29
    • 0009931174 scopus 로고    scopus 로고
    • A free-boundary model for diffusion-induced grain boundary motion
    • FIFE, P. C., CAHN, J. W. & ELLIOTT, C. M. (2001) A free-boundary model for diffusion-induced grain boundary motion. Interfaces Free Bound., 3, 291-336. (Pubitemid 33302888)
    • (2001) Interfaces and free boundaries , vol.3 , Issue.3 , pp. 291-336
    • Fife, P.C.1    Cahn, J.W.2    Elliott, C.M.3
  • 30
    • 61349134088 scopus 로고    scopus 로고
    • Multigrid methods for obstacle problems
    • GR̈ASER, C. & KORNHUBER, R. (2009) Multigrid methods for obstacle problems. J. Comput. Math., 27, 1-44.
    • (2009) J. Comput. Math. , vol.27 , pp. 1-44
    • Gr̈aser, C.1    Kornhuber, R.2
  • 31
    • 33646157612 scopus 로고    scopus 로고
    • An improvement of a recent Eulerian method for solving PDEs on general geometries
    • DOI 10.1007/s10915-005-9012-5
    • GREER, J. B. (2006) An improvement of a recent Eulerian method for solving PDEs on general geometries. J. Sci. Comput., 29, 321-352. (Pubitemid 44916351)
    • (2006) Journal of Scientific Computing , vol.29 , Issue.3 , pp. 321-352
    • Greer, J.B.1
  • 32
    • 33646143528 scopus 로고    scopus 로고
    • Fourth order partial differential equations on general geometries
    • DOI 10.1016/j.jcp.2005.11.031, PII S0021999105005498
    • GREER, J. B., BERTOZZI, A. L. & SAPIRO, G. (2006) Fourth order partial differential equations on general geometries. J. Comput. Phys., 216, 216-246. (Pubitemid 43632557)
    • (2006) Journal of Computational Physics , vol.216 , Issue.1 , pp. 216-246
    • Greer, J.B.1    Bertozzi, A.L.2    Sapiro, G.3
  • 33
    • 8744235083 scopus 로고    scopus 로고
    • A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
    • DOI 10.1016/j.jcp.2004.06.013, PII S002199910400261X
    • JAMES, A. J. & LOWENGRUB, J. (2004) A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J. Comput. Phys., 201, 685-722. (Pubitemid 39518803)
    • (2004) Journal of Computational Physics , vol.201 , Issue.2 , pp. 685-722
    • James, A.J.1    Lowengrub, J.2
  • 34
    • 42349110086 scopus 로고    scopus 로고
    • Finite element approximation of a Cahn-Hilliard-Navier-Stokes system
    • KAY, D. A., STYLES, V. & WELFORD, R. (2008) Finite element approximation of a Cahn-Hilliard-Navier-Stokes system. Interfaces Free Bound., 10, 15-43.
    • (2008) Interfaces Free Bound. , vol.10 , pp. 15-43
    • Kay, D.A.1    Styles, V.2    Welford, R.3
  • 35
    • 45449097630 scopus 로고    scopus 로고
    • An immersed boundary method for interfacial flows with insoluble surfactant
    • LAI, M.-C., TSENG, Y.-H. & HUANG, H. (2008) An immersed boundary method for interfacial flows with insoluble surfactant. J. Comput. Phys., 227, 7279-7293.
    • (2008) J. Comput. Phys. , vol.227 , pp. 7279-7293
    • Lai, M.-C.1    Tseng, Y.-H.2    Huang, H.3
  • 36
    • 34249715228 scopus 로고    scopus 로고
    • Surface phase separation and flow in a simple model of multicomponent drops and vesicles
    • LOWENGRUB, J., XU, J.-J. AND VOIGT, A. (2007) Surface phase separation and flow in a simple model of multicomponent drops and vesicles. Fluid Dyn. Mater. Process., 3, 1-20.
    • (2007) Fluid Dyn. Mater. Process. , vol.3 , pp. 1-20
    • Lowengrub, J.1    Xu, J.-J.2    Voigt, A.3
  • 37
    • 49749140110 scopus 로고    scopus 로고
    • Level set equations on surfaces via the closest point method
    • MACDONALD, C. B. & RUUTH, S. J. (2008) Level set equations on surfaces via the closest point method. J. Sci. Comput., 35, 219-240.
    • (2008) J. Sci. Comput. , vol.35 , pp. 219-240
    • MacDonald, C.B.1    Ruuth, S.J.2
  • 38
    • 79951508143 scopus 로고    scopus 로고
    • The implicit closest point method for the numerical solution of partial differential equations on surfaces
    • MACDONALD, C. B. & RUUTH, S. J. (2009) The implicit closest point method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput., 31, 4330-4350.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 4330-4350
    • MacDonald, C.B.1    Ruuth, S.J.2
  • 39
    • 0037952306 scopus 로고    scopus 로고
    • Classical solutions for diffusion-induced grain-boundary motion
    • MAYER, U. F. & SIMONETT, G. (1999) Classical solutions for diffusion-induced grain-boundary motion. J. Math. Anal. Appl., 234, 660-674.
    • (1999) J. Math. Anal. Appl. , vol.234 , pp. 660-674
    • Mayer, U.F.1    Simonett, G.2
  • 40
    • 0011424112 scopus 로고
    • Optimal interface error estimates for the mean curvature flow
    • NOCHETTO, R. H., PAOLINI, M. & VERDI, C. (1994) Optimal interface error estimates for the mean curvature flow. Ann. Sc. Norm. Super. Pisa, 21, 193-212.
    • (1994) Ann. Sc. Norm. Super. Pisa , vol.21 , pp. 193-212
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 41
    • 72749084586 scopus 로고    scopus 로고
    • A finite element method for surface PDEs: Matrix properties
    • OLSHANSKII, M. A. & REUSKEN, A. (2010) A finite element method for surface PDEs: matrix properties. Numer. Math., 114, 491-520.
    • (2010) Numer. Math. , vol.114 , pp. 491-520
    • Olshanskii, M.A.1    Reusken, A.2
  • 42
    • 70350169333 scopus 로고    scopus 로고
    • A finite element method for elliptic equations on surfaces
    • OLSHANSKII, M. A., REUSKEN, A. & GRANDE, J. (2009) A finite element method for elliptic equations on surfaces. SIAM J. Numer. Anal., 47, 3339-3358.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 3339-3358
    • Olshanskii, M.A.1    Reusken, A.2    Grande, J.3
  • 43
    • 3042841518 scopus 로고    scopus 로고
    • Level set methods and dynamic implicit surfaces
    • New York: Springer
    • OSHER, S. & FEDKIW, R. (2003) Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences. New York: Springer.
    • (2003) Applied Mathematical Science
    • Osher, S.1    Fedkiw, R.2
  • 44
    • 34548678944 scopus 로고    scopus 로고
    • PDE's on surfaces-a diffuse interface approach
    • R̈ATZ, A. & VOIGT, A. (2006) PDE's on surfaces-a diffuse interface approach. Commun. Math. Sci., 4, 575-590.
    • (2006) Commun. Math. Sci. , vol.4 , pp. 575-590
    • R̈atz, A.1    Voigt, A.2
  • 45
    • 37249003717 scopus 로고    scopus 로고
    • A simple embedding method for solving partial differential equations on surfaces
    • RUUTH, S. J. & MERRIMAN, B. (2008) A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys., 227, 1943-1961.
    • (2008) J. Comput. Phys. , vol.227 , pp. 1943-1961
    • Ruuth, S.J.1    Merriman, B.2
  • 46
    • 27144549033 scopus 로고    scopus 로고
    • Design of adaptive finite element software: The finite element toolbox ALBERTA
    • Berlin: Springer
    • SCHMIDT, A. & SIEBERT, K. G. (2005) Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA. Lecture Notes in Computational Science and Engineering, vol. 42. Berlin: Springer.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.42
    • Schmidt, A.1    Siebert, K.G.2
  • 49
    • 55149117088 scopus 로고    scopus 로고
    • A level set approach to anisotropic surface evolution with free adatoms
    • ST̈OCKER, C. & VOIGT, A. (2008a) A level set approach to anisotropic surface evolution with free adatoms. SIAM J. Appl. Math., 69, 64-80.
    • (2008) SIAM J. Appl. Math. , vol.69 , pp. 64-80
    • Sẗocker, C.1    Voigt, A.2
  • 50
    • 77954818584 scopus 로고    scopus 로고
    • Geodesic evolution laws-a level-set approach
    • ST̈OCKER, C. & VOIGT, A. (2008b) Geodesic evolution laws-a level-set approach. SIAM J. Imaging Sci., 1, 379-399.
    • (2008) SIAM J. Imaging Sci. , vol.1 , pp. 379-399
    • Sẗocker, C.1    Voigt, A.2
  • 51
    • 77953939478 scopus 로고    scopus 로고
    • A diffuse-interface approach for modelling transport diffusion and adsorption/desorption of material quantities on a deformable interface
    • TEIGEN, K. E., LI, X., LOWENGRUB, J., WANG, F. & VOIGT, A. (2009) A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Commun. Math. Sci., 7, 1009-1037.
    • (2009) Commun. Math. Sci. , vol.7 , pp. 1009-1037
    • Teigen, K.E.1    X, L.I.2    Lowengrub, J.3    Wang, F.4    Voigt, A.5
  • 52
    • 0346640322 scopus 로고    scopus 로고
    • An Eulerian formulation for solving partial differential equations along a moving interface
    • XU, J.-J. & ZHAO, H.-K. (2003) An Eulerian formulation for solving partial differential equations along a moving interface. J. Sci. Comput., 19, 573-594.
    • (2003) J. Sci. Comput. , vol.19 , pp. 573-594
    • Xu, J.-J.1    Zhao, H.-K.2


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