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Interpolation remainder theory from taylor expansions on triangles

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Summary

The constants in Sobolev norm error bounds are derived for interpolation remainders on triangles. These bounds can be applied to the finite element analysis of elliptic equations on a triangulation of a polygonal region Ω.

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References

  1. Barnhill, R. E., Gregory, J. A.: Sard kernel theorems on triangular domains with application to finite element error bounds. Numer. Math.25, 215–229 (1976)

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  2. Barnhill, R. E., Wilcox, C. H.: Computable finite element error bounds in terms of the boundary data. (To appear)

  3. Birkhoff, G., Schultz, M. H., Varga, R. S.: Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math.11, 232–256 (1968)

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  4. Gregory, J. A.: Piecewise interpolation theory for functions of two variables. Ph.D. thesis, Brunel University, Uxbridge, Middlesex, England, 1975

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  5. Sard, A.: Linear Approximation. Math. Surveys No. 9, Amer. Math. Soc., Providence, R. I., 1963. MR 28 # 1429.

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Authors and Affiliations

  1. Mathematics Department, University of Utah, 84112, Salt Lake City, Utah, USA

    Robert E. Barnhill

  2. Mathematics Department, Brunel University, Uxbridge, Middlesex, England

    John A. Gregory

Authors
  1. Robert E. Barnhill
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  2. John A. Gregory
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Additional information

The research of R. E. Barnhill was supported by The National Science Foundation with Grant GP 20293 to the University of Utah, the Science Research Council with Grants B/SR/9652 at Brunel University, and B/RG/61876 at Dundee University, a N.A.T.O. Senior Fellowship in Science, and the University of Utah Research Committee.

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Barnhill, R.E., Gregory, J.A. Interpolation remainder theory from taylor expansions on triangles. Numer. Math. 25, 401–408 (1975). https://doi.org/10.1007/BF01396336

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  • DOI: https://doi.org/10.1007/BF01396336

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