Numerische Mathematik

, Volume 25, Issue 3, pp 215–229 | Cite as

Sard kernel theorems on triangular domains with application to finite element error bounds

  • Robert E. Barnhill
  • John A. Gregory


Error bounds for interpolation remainders on triangles are derived by means of extensions of the Sard Kernel Theorems. These bounds are applied to the Galerkin method for elliptic boundary value problems. Certain kernels are shown to be identically zero under hypotheses which are, for example, fulfilled by tensor product interpolants on rectangles. This removes certain restrictions on how the sides of the triangles and/or rectangles tend to zero. Explicit error bounds are computed for piecewise linear interpolation over a triangulation and applied to a model problem.


Mathematical Method Tensor Product Linear Interpolation Galerkin Method Model Problem 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Robert E. Barnhill
    • 1
  • John A. Gregory
    • 2
  1. 1.Mathematics DepartmentUniversity of UtahSalt Lake CityUSA
  2. 2.Mathematics DepartmentBrunel UniversityUxbridgeEngland

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