Finite Element Interpolation

  • Alexandre Ern
  • Jean-Luc Guermond
Part of the Applied Mathematical Sciences book series (AMS, volume 159)


This chapter introduces the concept of finite elements along with the corresponding interpolation techniques. As an introductory example, we study how to interpolate functions in one dimension. Finite elements are then defined in arbitrary dimension, and numerous examples of scalar- and vector-valued finite elements are presented. Next, the concepts underlying the construction of meshes, approximation spaces, and interpolation operators are thoroughly investigated. The last sections of this chapter are devoted to the analysis of interpolation errors and inverse inequalities.


Interpolation Error Approximation Space Interpolation Operator Local Degree Elemental Mass Matrix 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Alexandre Ern
    • 1
  • Jean-Luc Guermond
    • 2
  1. 1.CERMICS, ENPCMarne la Vallée cedex 2France
  2. 2.LIMSI, CNRSOrsay cedexFrance

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