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
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)
Barnhill, R. E., Wilcox, C. H.: Computable finite element error bounds in terms of the boundary data. (To appear)
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)
Gregory, J. A.: Piecewise interpolation theory for functions of two variables. Ph.D. thesis, Brunel University, Uxbridge, Middlesex, England, 1975
Sard, A.: Linear Approximation. Math. Surveys No. 9, Amer. Math. Soc., Providence, R. I., 1963. MR 28 # 1429.
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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