4. Continuous Element for 2D Problems

  1. Pavel Šolín

Published Online: 30 NOV 2005

DOI: 10.1002/0471764108.ch4

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method

How to Cite

Šolín, P. (2005) Continuous Element for 2D Problems, in Partial Differential Equations and the Finite Element Method, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471764108.ch4

Publication History

  1. Published Online: 30 NOV 2005
  2. Published Print: 4 NOV 2005

ISBN Information

Print ISBN: 9780471720706

Online ISBN: 9780471764106

SEARCH

Summary

Chapter 4 explains in detail the finite element discretization of PDEs in two spatial dimensions. Discussed are approximation steps leading from a PDE problem to an approximate weak formulation, including those where traditionally the variational framework is violated (variational crimes). The transformation of the weak formulation to the reference domains is presented, and efficient evaluation of the stiffness integrals is discussed. Higher-order Gaussian quadrature rules in 2D are introduced. Modern higher-order nodal finite elements based on the product Gauss-Lobatto points (on quads) and on the Fekete points (on triangles) are discussed. Data structures, connectivity algorithms and assembling algorithms are presented. The Lagrange interpolation on the higher-order nodal elements is discussed.