메뉴 건너뛰기




Volumn 46, Issue 1-2, 2010, Pages 61-73

An anisotropic mesh adaptation method for the finite element solution of variational problems

Author keywords

Anisotropic mesh adaptation; Finite element; Mesh adaptation; Variational problem

Indexed keywords

ADAPTIVE MESHES; ANISOTROPIC FEATURES; ANISOTROPIC MESH ADAPTATION; EXACT SOLUTION; FINITE ELEMENT MESHES; FINITE ELEMENT SOLUTION; INTERPOLATION ERROR; ISOTROPIC MESH; MESH ADAPTATION; METRIC TENSOR; NUMERICAL RESULTS; POSTERIORI; UNIFORM MESH; VARIATIONAL PROBLEMS;

EID: 71549132198     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2009.06.012     Document Type: Article
Times cited : (14)

References (51)
  • 2
    • 0037143105 scopus 로고    scopus 로고
    • Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part II: structured grids
    • Ait-Ali-Yahia D., Baruzzi G., Habashi W.G., Fortin M., Dompierre J., and Vallet M.-G. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part II: structured grids. Int. J. Numer. Methods Fluids 39 (2002) 657-673
    • (2002) Int. J. Numer. Methods Fluids , vol.39 , pp. 657-673
    • Ait-Ali-Yahia, D.1    Baruzzi, G.2    Habashi, W.G.3    Fortin, M.4    Dompierre, J.5    Vallet, M.-G.6
  • 3
    • 0003918275 scopus 로고    scopus 로고
    • Anisotropic finite elements: local estimates and applications
    • B.G. Teubner, Stuttgart, Leipzig
    • Apel T. Anisotropic finite elements: local estimates and applications. Series of Advances in Numerical Mathematics (1999), B.G. Teubner, Stuttgart, Leipzig
    • (1999) Series of Advances in Numerical Mathematics
    • Apel, T.1
  • 4
    • 0026626564 scopus 로고
    • Anisotropic interpolation with applications to the finite element method
    • Apel T., and Dobrowolski M. Anisotropic interpolation with applications to the finite element method. Computing 47 (1992) 277-293
    • (1992) Computing , vol.47 , pp. 277-293
    • Apel, T.1    Dobrowolski, M.2
  • 5
    • 0011235023 scopus 로고    scopus 로고
    • A variational method in image recovery
    • Aubert G., and Vese L. A variational method in image recovery. SIAM J. Numer. Anal. 34 (1997) 1948-1979
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1948-1979
    • Aubert, G.1    Vese, L.2
  • 7
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: basic analysis and examples
    • Becker R., and Rannacher R. A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J. Numer. Math. 4 (1996) 237-264
    • (1996) East-West J. Numer. Math. , vol.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 8
    • 85022001969 scopus 로고    scopus 로고
    • An optimal control approach to a posteriori error estimation in finite element methods
    • Becker R., and Rannacher R. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1-102
    • (2001) Acta Numer. , vol.10 , pp. 1-102
    • Becker, R.1    Rannacher, R.2
  • 9
    • 0042041100 scopus 로고    scopus 로고
    • Local error estimates and adaptive refinement for first-order system least squares (FOSLS)
    • Berndt M., Manteuffel T.A., and Mccormick S.F. Local error estimates and adaptive refinement for first-order system least squares (FOSLS). Electr. Trans. Numer. Anal. 6 (1997) 35-43
    • (1997) Electr. Trans. Numer. Anal. , vol.6 , pp. 35-43
    • Berndt, M.1    Manteuffel, T.A.2    Mccormick, S.F.3
  • 11
    • 17444403192 scopus 로고    scopus 로고
    • On the finite element solution of the pure Neumann problem
    • Bochev P., and Lehoucq R.B. On the finite element solution of the pure Neumann problem. SIAM Rev. 47 (2005) 50-66
    • (2005) SIAM Rev. , vol.47 , pp. 50-66
    • Bochev, P.1    Lehoucq, R.B.2
  • 13
    • 0031099169 scopus 로고    scopus 로고
    • Delaunay mesh generation governed by metric specification: part II. Applications
    • Borouchaki H., George P.L., and Mohammadi B. Delaunay mesh generation governed by metric specification: part II. Applications. Finite Elem. Anal. Des. 25 (1997) 85-109
    • (1997) Finite Elem. Anal. Des. , vol.25 , pp. 85-109
    • Borouchaki, H.1    George, P.L.2    Mohammadi, B.3
  • 14
    • 71549172001 scopus 로고    scopus 로고
    • F.J. Bossen, P.S. Heckbert, A pliant method for anisotropic mesh generation, in: Proceedings of the Fifth International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 1996, pp. 63-74, Sandia Report 96-2301.
    • F.J. Bossen, P.S. Heckbert, A pliant method for anisotropic mesh generation, in: Proceedings of the Fifth International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 1996, pp. 63-74, Sandia Report 96-2301.
  • 15
    • 0028747782 scopus 로고
    • First-order system least squares for second-order partial differential equations: part I
    • Cai Z., Lazarov R., Manteuffel T.A., and Mccormick S.F. First-order system least squares for second-order partial differential equations: part I. SIAM J. Numer. Anal. 31 (1994) 1785-1799
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1785-1799
    • Cai, Z.1    Lazarov, R.2    Manteuffel, T.A.3    Mccormick, S.F.4
  • 16
    • 2342588708 scopus 로고    scopus 로고
    • First-order system least squares for the stress-displacement formulation: linear elasticity
    • Cai Z., and Starke G. First-order system least squares for the stress-displacement formulation: linear elasticity. SIAM J. Numer. Anal. 41 (2003) 715-730
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 715-730
    • Cai, Z.1    Starke, G.2
  • 17
    • 10144254912 scopus 로고    scopus 로고
    • Least-squares methods for linear elasticity
    • Cai Z., and Starke G. Least-squares methods for linear elasticity. SIAM J. Numer. Anal. 42 (2004) 826-842
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 826-842
    • Cai, Z.1    Starke, G.2
  • 19
    • 0031377806 scopus 로고    scopus 로고
    • Local error estimation and adaptive remeshing scheme for least-squares mixed finite elements
    • Carey G.F., and Pehlivanov A. Local error estimation and adaptive remeshing scheme for least-squares mixed finite elements. Comput. Methods Appl. Mech. Eng. 150 (1997) 125-131
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.150 , pp. 125-131
    • Carey, G.F.1    Pehlivanov, A.2
  • 21
    • 3042758075 scopus 로고    scopus 로고
    • Variational PDE models in image processing
    • Chan T.F., Shen J., and Vese L. Variational PDE models in image processing. Not. Am. Math. Soc. 50 (2003) 14-26
    • (2003) Not. Am. Math. Soc. , vol.50 , pp. 14-26
    • Chan, T.F.1    Shen, J.2    Vese, L.3
  • 22
    • 0026136907 scopus 로고
    • Numerical approximation of the solution of variational problem with a double well potential
    • Collins C., Kinderlehrer D., and Luskin M. Numerical approximation of the solution of variational problem with a double well potential. SIAM J. Numer. Anal. 28 (1991) 321-332
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 321-332
    • Collins, C.1    Kinderlehrer, D.2    Luskin, M.3
  • 23
    • 84966255684 scopus 로고
    • Optimal order estimates for the finite element approximation of the solution of a nonconvex variational problem
    • Collins C., and Luskin M. Optimal order estimates for the finite element approximation of the solution of a nonconvex variational problem. Math. Comput. 57 (1991) 621-637
    • (1991) Math. Comput. , vol.57 , pp. 621-637
    • Collins, C.1    Luskin, M.2
  • 24
    • 0000906086 scopus 로고
    • Optimal triangular mesh generation by coordinate transformation
    • D'Azevedo E.F. Optimal triangular mesh generation by coordinate transformation. SIAM J. Sci. Stat. Comput. 12 (1991) 755-786
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , pp. 755-786
    • D'Azevedo, E.F.1
  • 25
    • 0001043157 scopus 로고
    • On optimal triangular meshes for minimizing the gradient error
    • D'Azevedo E.F., and Simpson R.B. On optimal triangular meshes for minimizing the gradient error. Numer. Math. 59 (1991) 321-348
    • (1991) Numer. Math. , vol.59 , pp. 321-348
    • D'Azevedo, E.F.1    Simpson, R.B.2
  • 26
    • 0346197481 scopus 로고
    • Existence de maillages optimaux dans les méthodes d'éléments finis
    • de Oliveira P. Existence de maillages optimaux dans les méthodes d'éléments finis. RAIRO Anal. Numér. 14 (1980) 279-290
    • (1980) RAIRO Anal. Numér. , vol.14 , pp. 279-290
    • de Oliveira, P.1
  • 27
    • 0037143094 scopus 로고    scopus 로고
    • Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part III: unstructured meshes
    • Dompierre J., Vallet M.-G., Bourgault Y., Fortin M., and Habashi W.G. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part III: unstructured meshes. Int. J. Numer. Methods Fluids 39 (2002) 675-702
    • (2002) Int. J. Numer. Methods Fluids , vol.39 , pp. 675-702
    • Dompierre, J.1    Vallet, M.-G.2    Bourgault, Y.3    Fortin, M.4    Habashi, W.G.5
  • 29
    • 0016993969 scopus 로고
    • Optimization of finite element grids by direct energy search
    • Felippa C.A. Optimization of finite element grids by direct energy search. Appl. Math. Modelling 1 (1976) 93-96
    • (1976) Appl. Math. Modelling , vol.1 , pp. 93-96
    • Felippa, C.A.1
  • 30
    • 49449126521 scopus 로고
    • Numerical experiments in finite element grid optimization by direct energy search
    • Felippa C.A. Numerical experiments in finite element grid optimization by direct energy search. Appl. Math. Modelling 1 (1977) 239-244
    • (1977) Appl. Math. Modelling , vol.1 , pp. 239-244
    • Felippa, C.A.1
  • 31
    • 0025416425 scopus 로고
    • On the convergence of finite-element approximations of a relaxed variational problem
    • French D.A. On the convergence of finite-element approximations of a relaxed variational problem. SIAM J. Numer. Anal. 27 (1990) 419-436
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 419-436
    • French, D.A.1
  • 33
    • 0005499929 scopus 로고    scopus 로고
    • Boundary layer meshing for viscous flows in complex domain
    • Sandia National Laboratories, Albuquerque, NM
    • R.V. Garimella, M.S. Shephard, Boundary layer meshing for viscous flows in complex domain, in: Proceedings of the Seventh International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 1998, pp. 107-118.
    • (1998) Proceedings of the Seventh International Meshing Roundtable , pp. 107-118
    • Garimella, R.V.1    Shephard, M.S.2
  • 34
    • 70350511699 scopus 로고    scopus 로고
    • Automatic mesh generation and finite element computation
    • Ciarlet P.G., and Lions J.L. (Eds), Elsevier Science B.V., New York
    • George P.L. Automatic mesh generation and finite element computation. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis vol. IV (1996), Elsevier Science B.V., New York 69-190
    • (1996) Handbook of Numerical Analysis , vol.IV , pp. 69-190
    • George, P.L.1
  • 35
    • 0028380768 scopus 로고
    • Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions
    • Gremaud P.A. Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions. SIAM J. Numer. Anal. 31 (1994) 111-127
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 111-127
    • Gremaud, P.A.1
  • 36
    • 0034161524 scopus 로고    scopus 로고
    • Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles
    • Habashi W.G., Dompierre J., Bourgault Y., Ait-Ali-Yahia D., Fortin M., and Vallet M.-G. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles. Int. J. Numer. Methods Fluids 32 (2000) 725-744
    • (2000) Int. J. Numer. Methods Fluids , vol.32 , pp. 725-744
    • Habashi, W.G.1    Dompierre, J.2    Bourgault, Y.3    Ait-Ali-Yahia, D.4    Fortin, M.5    Vallet, M.-G.6
  • 37
    • 0004322654 scopus 로고    scopus 로고
    • Bidimensional anisotropic mesh generator
    • Technical report, INRIA, Rocquencourt, 1997. Source code
    • F. Hecht, Bidimensional anisotropic mesh generator, Technical report, INRIA, Rocquencourt, 1997. Source code: 〈http://www.ann.jussieu.fr/hecht/ftp/bamg/〉.
    • Hecht, F.1
  • 38
    • 15944411787 scopus 로고    scopus 로고
    • Metric tensors for anisotropic mesh generation
    • Huang W. Metric tensors for anisotropic mesh generation. J. Comput. Phys. 204 (2005) 633-665
    • (2005) J. Comput. Phys. , vol.204 , pp. 633-665
    • Huang, W.1
  • 39
    • 33751100721 scopus 로고    scopus 로고
    • Mathematical principles of anisotropic mesh adaptation
    • Huang W. Mathematical principles of anisotropic mesh adaptation. Comm. Comput. Phys. 1 (2006) 276-310
    • (2006) Comm. Comput. Phys. , vol.1 , pp. 276-310
    • Huang, W.1
  • 40
    • 0023306448 scopus 로고
    • Adaptive refinement of least-squares finite elements with element-by-element conjugate gradient solution
    • Jiang B.N., and Carey G.F. Adaptive refinement of least-squares finite elements with element-by-element conjugate gradient solution. Int. J. Numer. Methods Eng. 24 (1987) 569-580
    • (1987) Int. J. Numer. Methods Eng. , vol.24 , pp. 569-580
    • Jiang, B.N.1    Carey, G.F.2
  • 43
    • 0027684524 scopus 로고
    • An anisotropic h-type mesh refinement strategy
    • Rachowicz W. An anisotropic h-type mesh refinement strategy. Comput. Methods Appl. Mech. Eng. 109 (1993) 169-181
    • (1993) Comput. Methods Appl. Mech. Eng. , vol.109 , pp. 169-181
    • Rachowicz, W.1
  • 44
    • 14344265344 scopus 로고    scopus 로고
    • Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods
    • Remacle J., Li X., Shephard M.S., and Flaherty J.E. Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int. J. Numer. Methods Eng. 62 (2003) 899-923
    • (2003) Int. J. Numer. Methods Eng. , vol.62 , pp. 899-923
    • Remacle, J.1    Li, X.2    Shephard, M.S.3    Flaherty, J.E.4
  • 45
    • 0030530686 scopus 로고    scopus 로고
    • An a posteriori error estimator for anisotropic refinement
    • Siebert K.G. An a posteriori error estimator for anisotropic refinement. Numer. Math. 73 (1996) 373-398
    • (1996) Numer. Math. , vol.73 , pp. 373-398
    • Siebert, K.G.1
  • 47
    • 0000816388 scopus 로고    scopus 로고
    • A new moving mesh algorithm for the finite element solution of variational problems
    • (electronic)
    • Tourigny Y., and Hülsemann F. A new moving mesh algorithm for the finite element solution of variational problems. SIAM J. Numer. Anal. 35 (1998) 1416-1438 (electronic)
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1416-1438
    • Tourigny, Y.1    Hülsemann, F.2
  • 48
    • 71549124457 scopus 로고    scopus 로고
    • S. Yamakawa, K. Shimada, High quality anisotropic tetrahedral mesh generation via ellipsoidal bubble packing, in: Proceedings of the Ninth International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 2000, pp. 263-273, Sandia Report 2000-2207.
    • S. Yamakawa, K. Shimada, High quality anisotropic tetrahedral mesh generation via ellipsoidal bubble packing, in: Proceedings of the Ninth International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 2000, pp. 263-273, Sandia Report 2000-2207.
  • 49
    • 23844471344 scopus 로고    scopus 로고
    • A new finite element gradient recovery method: superconvergence property
    • Zhang Z., and Naga A. A new finite element gradient recovery method: superconvergence property. SIAM J. Sci. Comput. 26 (2005) 1192-1213
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 1192-1213
    • Zhang, Z.1    Naga, A.2
  • 50
    • 0026866050 scopus 로고
    • The superconvergence patch recovery and a posteriori error estimates. Part 1: the recovery technique
    • Zienkiewicz O.C., and Zhu J.Z. The superconvergence patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int. J. Numer. Methods Eng. 33 (1992) 1331-1364
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 51
    • 0026869285 scopus 로고
    • The superconvergence patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity
    • Zienkiewicz O.C., and Zhu J.Z. The superconvergence patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity. Int. J. Numer. Methods Eng. 33 (1992) 1365-1382
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 1365-1382
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.