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Volumn 26, Issue 5, 2005, Pages 1643-1666

Measuring mesh qualities and application to variational mesh adaptation

Author keywords

Error estimate; Mesh adaptation; Mesh quality; Variational mesh adaptation

Indexed keywords

ERROR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING; PRODUCT DEVELOPMENT; QUALITY ASSURANCE;

EID: 25444533561     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827503429405     Document Type: Article
Times cited : (44)

References (36)
  • 1
  • 2
    • 0003267718 scopus 로고    scopus 로고
    • Anisotropic finite elements: Local estimates and applications
    • B. G. Teubner Stuttgart, Liepzig
    • T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., B. G. Teubner Stuttgart, Liepzig, 1999.
    • (1999) Adv. Numer. Math.
    • Apel, T.1
  • 4
    • 0026626564 scopus 로고
    • Anisotropic interpolation with applications to the finite element method
    • T. APEL AND M. DOBROWOLSKI, Anisotropic interpolation with applications to the finite element method, Computing, 47 (1992), pp. 277-293.
    • (1992) Computing , vol.47 , pp. 277-293
    • Apel, T.1    Dobrowolski, M.2
  • 5
    • 0032045072 scopus 로고    scopus 로고
    • Anisotropic mesh refinement for a singularly perturbed reaction-diffusion model problem
    • T. APEL AND G. LUBE, Anisotropic mesh refinement for a singularly perturbed reaction-diffusion model problem, Appl. Numer. Math., 26 (1998), pp. 415-433.
    • (1998) Appl. Numer. Math. , vol.26 , pp. 415-433
    • Apel, T.1    Lube, G.2
  • 6
    • 0016939764 scopus 로고
    • On the angle condition in the finite element method
    • I. BABUŠKA AND A. K. Aziz, On the angle condition in the finite element method, SIAM J. Numer. Anal., 13 (1976), pp. 214-226.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 214-226
    • Babuška, I.1    Aziz, A.K.2
  • 7
    • 0032205858 scopus 로고    scopus 로고
    • A solution-based triangular and tetrahedral mesh quality indicator
    • M. BERZINS, A solution-based triangular and tetrahedral mesh quality indicator, SIAM J. Sci. Comput., 19 (1998), pp. 2051-2060.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 2051-2060
    • Berzins, M.1
  • 8
    • 0002255324 scopus 로고
    • An adaptive grid with directional control
    • J. U. BRACKBILL, An adaptive grid with directional control, J. Comput. Phys., 108 (1993), pp. 38-50.
    • (1993) J. Comput. Phys. , vol.108 , pp. 38-50
    • Brackbill, J.U.1
  • 9
    • 49049134162 scopus 로고
    • Adaptive zoning for singular problems in two dimensions
    • J. U. BRACKBILL AND J. S. SALTZMAN, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys., 46 (1982), pp. 342-368.
    • (1982) J. Comput. Phys. , vol.46 , pp. 342-368
    • Brackbill, J.U.1    Saltzman, J.S.2
  • 10
    • 0015960570 scopus 로고
    • Splines (with optimal knots) are better
    • H. G. BURCHARD, Splines (with optimal knots) are better, Appl. Anal., 3 (1974), pp. 309-319.
    • (1974) Appl. Anal. , vol.3 , pp. 309-319
    • Burchard, H.G.1
  • 12
    • 0000520595 scopus 로고    scopus 로고
    • Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes
    • V. DOLEJSI, Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes, Computing and Visualisation in Science, 1 (1998), pp. 165-178.
    • (1998) Computing and Visualisation in Science , vol.1 , pp. 165-178
    • Dolejsi, V.1
  • 13
    • 0000379994 scopus 로고
    • Adaptive grid generation from harmonic maps on Riemannian manifolds
    • A. S. DVINSKY, Adaptive grid generation from harmonic maps on Riemannian manifolds, J. Comput. Phys., 95 (1991), pp. 450-476.
    • (1991) J. Comput. Phys. , vol.95 , pp. 450-476
    • Dvinsky, A.S.1
  • 14
    • 0004239501 scopus 로고
    • Mathematical aspects of numerical grid generation
    • SIAM, Philadelphia
    • J. E. CASTILLO, ED., Mathematical Aspects of Numerical Grid Generation, Frontiers in Appl. Math. 8, SIAM, Philadelphia, 1991.
    • (1991) Frontiers in Appl. Math. , vol.8
    • Castillo, J.E.1
  • 15
    • 0000330572 scopus 로고
    • Grid adaption based on modified anisotropic diffusion equations formulated in the parametric domain
    • R. HAGMEEIJER, Grid adaption based on modified anisotropic diffusion equations formulated in the parametric domain, J. Comput. Phys., 115 (1994), pp. 169-183.
    • (1994) J. Comput. Phys. , vol.115 , pp. 169-183
    • Hagmeeijer, R.1
  • 17
    • 0000311286 scopus 로고    scopus 로고
    • Practical aspects of formulation and solution of moving mesh partial differential equations
    • W. HUANG, Practical aspects of formulation and solution of moving mesh partial differential equations, J. Comput. Phys., 171 (2001), pp. 753-775.
    • (2001) J. Comput. Phys. , vol.171 , pp. 753-775
    • Huang, W.1
  • 18
    • 0035842844 scopus 로고    scopus 로고
    • Variational mesh adaptation: Isotropy and equidistribution
    • W. HUANG, Variational mesh adaptation: Isotropy and equidistribution, J. Comput. Phys., 174 (2001), pp. 903-924.
    • (2001) J. Comput. Phys. , vol.174 , pp. 903-924
    • Huang, W.1
  • 19
    • 0037455650 scopus 로고    scopus 로고
    • Variational mesh adaptation II: Error estimates and monitor functions
    • W. HUANG AND W. SUN, Variational mesh adaptation II: Error estimates and monitor functions, J. Comput. Phys., 184 (2003), pp. 619-648.
    • (2003) J. Comput. Phys. , vol.184 , pp. 619-648
    • Huang, W.1    Sun, W.2
  • 20
    • 0016931650 scopus 로고
    • Estimations de l'erreur pour des elements finis droits preque degeneres
    • P. JAMET, Estimations de l'erreur pour des elements finis droits preque degeneres, RAIRO Anal. Numer., 10 (1976), pp. 43-60.
    • (1976) RAIRO Anal. Numer. , vol.10 , pp. 43-60
    • Jamet, P.1
  • 21
    • 0000712022 scopus 로고
    • Mesh generation using vector-fields
    • P. KNUPP, Mesh generation using vector-fields, J. Comput. Phys., 119 (1995), pp. 142-148.
    • (1995) J. Comput. Phys. , vol.119 , pp. 142-148
    • Knupp, P.1
  • 23
    • 0000870626 scopus 로고    scopus 로고
    • Jacobian-weighted elliptic grid generation
    • P. M. KNUPP, Jacobian-weighted elliptic grid generation, SIAM J. Sci. Comput., 17 (1996), pp. 1475-1490.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1475-1490
    • Knupp, P.M.1
  • 24
    • 0034505846 scopus 로고    scopus 로고
    • A framework for variational grid generation: Conditioning the Jacobian matrix with matrix norms
    • P. M. KNUPP AND N. ROBIDOUX, A framework for variational grid generation: Conditioning the Jacobian matrix with matrix norms, SIAM J. Sci. Comput., 21 (2000), pp. 2029-2047.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2029-2047
    • Knupp, P.M.1    Robidoux, N.2
  • 25
    • 84968510078 scopus 로고
    • On the arithmetic and geometric means and on Holder's inequality
    • H. KOBER, On the arithmetic and geometric means and on Holder's inequality, Proc. Amer. Math. Soc., 9 (1958), pp. 452-459.
    • (1958) Proc. Amer. Math. Soc. , vol.9 , pp. 452-459
    • Kober, H.1
  • 26
    • 0026841003 scopus 로고
    • On the maximum angle condition for linear tetrahedral elements
    • M. KŘÍŽEK, On the maximum angle condition for linear tetrahedral elements, SIAM J. Numer. Anal., 29 (1992), pp. 513-520.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 513-520
    • Křížek, M.1
  • 32
    • 49949139816 scopus 로고
    • Numerical solution of the quasi-linear Poisson equation in a nonuniform triangle mesh
    • A. WINSLOW, Numerical solution of the quasi-linear Poisson equation in a nonuniform triangle mesh, J. Comput. Phys., 1 (1967), pp. 149-172.
    • (1967) J. Comput. Phys. , vol.1 , pp. 149-172
    • Winslow, A.1
  • 33
    • 84882387282 scopus 로고    scopus 로고
    • A new finite element gradient recovery method, Part I: Superconvergence property
    • to appear
    • Z. ZHANG AND A. NAGA, A new finite element gradient recovery method, Part I: Superconvergence property, SIAM J. Sci. Comput., to appear.
    • SIAM J. Sci. Comput.
    • Zhang, Z.1    Naga, A.2
  • 34
    • 0026866050 scopus 로고
    • The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery technique
    • O.C. ZIENKIEWICZ AND J. Z. ZHU, The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Methods Engrg., 33 (1992), pp. 1331-1364.
    • (1992) Internat. J. Numer. Methods Engrg. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 35
    • 0026869285 scopus 로고
    • The superconvergence patch recovery and a posteriori error estimates. Part 2: Error esimates and adaptivity
    • O.C. ZIENKIEWICZ AND J. Z. ZHU, The superconvergence patch recovery and a posteriori error estimates. Part 2: Error esimates and adaptivity, Internat. J. Numer. Methods Engrg., 33 (1992), pp.1365-1382.
    • (1992) Internat. J. Numer. Methods Engrg. , vol.33 , pp. 1365-1382
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 36
    • 0000466572 scopus 로고
    • On the finite element method
    • M. ZLÁMAL, On the finite element method, Numer. Math., 12 (1968), pp. 394-409.
    • (1968) Numer. Math. , vol.12 , pp. 394-409
    • Zlámal, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.