Constructing general reference finite elements

  • Robert C. Kirby
  • Kent-Andre Mardal
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 84)


This chapter describes the mathematical framework for constructing a general class of finite elements on reference domains. This framework is used by both the FIAT and SyFi projects, see the Chapters 13 and 15, respectively. Our goal is to provide a framework by which simplicial finite elements with very complicated bases can be constructed automatically. We work from the classic Ciarlet definition of the finite element and its “nodal” basis (an abstract notion far more general and powerful than standard node-oriented Lagrange polynomials).


General Reference Legendre Polynomial Jacobi Polynomial Reference Element Nodal Basis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Robert C. Kirby
    • 1
  • Kent-Andre Mardal
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Center for Biomedical Computing at Simula Research LaboratoryOsloNorway
  3. 3.Department of InformaticsUniversity of OsloOsloNorway

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