hp-Finite Element Procedures on Non-Uniform Geometric Meshes: Adaptivity and Constrained Approximation

  • Mark Ainsworth
  • Bill Senior
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 113)

Abstract

A simple adaptive hp-finite element procedure is described for linear elliptic boundary value problems on polygonal domains. A methodology is given for implementing the constrained hp-refinements on the highly graded meshes needed to achieve optimal exponential rates of convergence. Numerical examples confirm that the sequence of adaptively designed meshes closely tracks the curves that define the proper combination of hp-refinements. Thus, the adaptive procedure produces near optimal meshes and achieves an exponential rate of convergence.

Key words

hp-version finite element method Adaptive refinement Constrained approximation 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Mark Ainsworth
    • 1
  • Bill Senior
    • 1
  1. 1.Mathematics DepartmentLeicester UniversityLeicesterUK

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