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A mesh optimization algorithm to decrease the maximum interpolation error of linear triangular finite elements

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Abstract

We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh optimization algorithm can reduce the W 1,∞ semi-norm of the interpolation error. For these examples, the L 2, L ∞, and H 1 norms decreased also.

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Notes

  1. In the numerical experiments, this search is implemented with a simple loop through the elements of the background mesh.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, P.O. Box 352420, Seattle, WA, 98195-2420, USA

    U. Hetmaniuk

  2. Sandia National Laboratories, P.O. Box 5800, MS 1318, Albuquerque, NM, 87185-1318, USA

    P. Knupp

Authors
  1. U. Hetmaniuk
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  2. P. Knupp
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Correspondence to U. Hetmaniuk.

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Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

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Hetmaniuk, U., Knupp, P. A mesh optimization algorithm to decrease the maximum interpolation error of linear triangular finite elements. Engineering with Computers 27, 3–15 (2011). https://doi.org/10.1007/s00366-010-0176-8

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  • DOI: https://doi.org/10.1007/s00366-010-0176-8

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