The purpose of this paper is to determine more nearly computable error bounds for finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. In the appropriate norm, the interpolation remainder is an upper bound on the finite element remainder. This follows from a best approximation property of finite element solution (Section 2). The SARD kernel theorems [7] provide representations of admissible linear functionals defined on function spaces of prescribed smoothness. These theorems are defined for rectangles and in Section 4 are extended to triangles. The method can be extended to more general regions [1]. In this paper we calculate the constants in interpolation error bounds for triangles. This is done in Section 5 for the particular case of piecewise linear interpolation. Finally in Section 6 the results of Section 5 are applied to a specific boundary value problem in order to obtain numerical results.


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Copyright information

© Springer Basel AG 1974

Authors and Affiliations

  • R. E. Barnhill
    • 1
  • J. R. Whiteman
    • 2
  1. 1.Salt Lake CityUSA
  2. 2.UxbridgeUK

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