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Isotropic refinement and recoarsening in two dimensions

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Abstract

In this paper we describe an implementation of the isotropic red-green refinement technique for two-dimensional triangulations as described in [1] and [5]. In addition, we present a new method for local recoarsening of a previously refined mesh. Furthermore, we explain some techniques to interpolate data while manipulating a grid.

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References

  1. R. E. Bank, A. H. Sherman and A. Weiser, Refinement algorithms and data structures for regular local mesh refinements, in:Scientific Computing, eds. R. Stepleman et al. (IMACS, North-Holland, Amsterdam, 1983) pp. 3–17.

    Google Scholar 

  2. E. Bänsch, Local mesh refinement in 2 and 3 dimensions, Impact Comput. Sci. Engrg. 3 (1991) 181–191.

    Google Scholar 

  3. E. Bänsch, An adaptive finite-element-strategy for the 3D time-dependent Navier-Stokes-equations, J. Comput. Appl. Math. 36 (1991) 3–28.

    Google Scholar 

  4. F. Bornemann, B. Erdmann and R. Kornhuber, Adaptive multilevel methods in three space dimensions, Internat. J. Numer. Methods Engrg. 36 (1993) 3187–3203.

    Google Scholar 

  5. P. Deuflhard, P. Leinen and H. Yserentant, Concepts of an adaptive hierarchical finite element code, Impact Comput. Sci. Engrg. 1 (1989) 3–35.

    Google Scholar 

  6. O. Friedrich, A new method for generating inner points of triangulations in two dimensions, Comput. Methods Appl. Mech. Engrg. 104 (1993) 77–86.

    Google Scholar 

  7. D. Hempel, Local mesh adaptation in two space dimensions, Impact Comput. Sci. Engrg. 5 (1993) 309–317.

    Google Scholar 

  8. T. Sonar, On the design of an upwind scheme for compressible flow on general triangulations, Numer. Algorithms 4 (1993) 135–149.

    Google Scholar 

  9. T. Sonar, V. Hannemann and D. Hempel, Dynamic adaptivity and residual control in unsteady compressible flow computation, Math. Comput. Modelling 20 (1994) 201–213.

    Google Scholar 

  10. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115–173.

    Google Scholar 

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Communicated by G. Mühlbach

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Hempel, D. Isotropic refinement and recoarsening in two dimensions. Numer Algor 13, 33–43 (1996). https://doi.org/10.1007/BF02143125

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  • DOI: https://doi.org/10.1007/BF02143125

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