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A modified bubble placement method and its application in solving elliptic problem with discontinuous coefficients adaptively

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Pages 1268-1289 | Received 23 Jun 2015, Accepted 05 Apr 2016, Published online: 24 May 2016

References

  • S. Arya, D.M. Mount, N.S. Netanyahu, R. Silverman, and A.Y. Wu, An optimal algorithm for approximate nearest neighbor searching fixed dimensions, J. ACM. 45 (1998), pp. 891–923.
  • R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput. 44 (1985), pp. 283–301.
  • C. Bernardi and R. Verfrth, Adapive finite element methods for elliptic equations with non-smooth coefficients, J. Numer. Math. 85 (2000), pp. 579–608.
  • A. Bonito, R.A. DeVore, and R.H. Nochetto, Adaptive finite element methods for elliptic problems with discontinuous coefficients, SIAM J. Numer. Anal. 51 (2013), pp. 3106–3134.
  • Z.Q. Cai and S. Zhang, Recovery-based error estimator for interface problems: conforming linear elements, SIAM J. Numer. Anal. 47 (2009), pp. 2132–2156.
  • W.W. Chen, Y.F. Nie, W.W. Zhang, and L. Wang, A fast local mesh generation method about high-quality node set, Chin. J. Comput. Mech. 29 (2012), pp. 704–709.
  • Z.M. Chen and S.B. Dai, On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients, SIAM J. Sci. Comput. 24 (2002), pp. 443–462.
  • F. Hecht, FreeFem++, version 3.21. Available at http://www.freefem.org/
  • F. Hecht, The mesh adapting software: bamg, INRIA report, 1998 (1998).
  • Y.Q. Huang, H.F. Qin, D.S. Wang, and Q. Du, Convergent adaptive finite element method based on centroidal voronoi tessellations and superconvergence, Commun. Comput. Phys. 10 (2011), pp. 339–370.
  • L.L. Ju, M. Gunzburger, and W.D. Zhao, Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi–Delaunay triangulations, SIAM J. Sci. Comput. 28 (2006), pp. 2023–2053.
  • Y. Liu, Y.F. Nie, W.W. Zhang, and L. Wang, Node placement method by bubble simulation and its application, CMES. 55 (2010), pp. 89–109.
  • P. Morin, R.H. Nochetto, and K.G. Siebert, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal. 38 (2000), pp. 466–488.
  • P.-O. Persson and G. Strang, A simple mesh generator in matlab, SIAM Rev. 46 (2004), pp. 329–345.
  • R.D. Peter Binev, Fast computation in adaptive tree approximation, Numer. Math. 97 (2004), pp. 193–217.
  • M. Petzoldt, A posteriori error estimators for elliptic equations with discontinuous coefficients, Adv. Comput. Math 16 (2002), pp. 47–75.
  • N. Qi, Y.F. Nie, and W.W. Zhang, Acceleration strategies based on an improved bubble packing method, Commun. Comput. Phys. 16 (2014), pp. 115–135.
  • K. Segeth, A review of some a posteriori error estimates for adaptive finite element methods, Math. Comput. Simul. 80 (2010), pp. 1589–1600.
  • K. Shimada and D.C. Gossard, Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis, Comput. Aided. Geom. D. 15 (1998), pp. 199–222.
  • R. Stevenson, The completion of locally refined simplicial partitions created by bisection, Math. Comput. 77 (2008), pp. 227–241.
  • R. Verfrth, A Review of a Posteriori Error Estimation and Adaptive Mesh Refinement Techniques, Wiley & Teubner, Stuttgart, 1996.
  • R.P. Zhang, X.J. Yu, and X. Cui, The weighted discontinuous Galerkin method for elliptic problem with jump coefficients, J. Numer. Methods Comput. Appl. 34 (2013), pp. 178–186.
  • W.W. Zhang, Y.F. Nie, and Y.T. Gu, Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation, J. Comput. Appl. Math. 280 (2015), pp. 42–58.
  • H.B. Zheng, Y.R. Hou, and F. Shi, Adaptive variational multiscale methods for incompressible flow based on two local Gauss integrations, J. Comput. Phys. 229 (2010), pp. 7030–7041.
  • O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery (spr) and adaptive finite element refinement, Comput. Method. Appl. Mech. 101 (1992), pp. 207–224.

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