Quadratures, Assembling, and Storage

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


This chapter deals with various aspects related to the implementation of the finite element method. It is organized into four sections. The first section is concerned with quadratures, i.e., methods to evaluate integrals approximately. These are almost unavoidable in applications since only a few academic problems involve integrals which can be evaluated analytically. We present various quadratures and evaluate the impact of this type of approximation on the accuracy of the finite element method. In the first section, we also list important arrays (Jacobian, shape functions, derivatives, etc.) which are required in a finite element code. The second section deals with assembling techniques for matrices and right-hand sides. The next section reviews some basic storage techniques for sparse matrices. In the last section, we briefly discuss how to deal with essential boundary conditions, whether homogeneous or not.


Shape Function Column Index Essential Boundary Condition Iterative Solution Method Krylov Space 
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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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