Finite element approximation on quadrilateral meshes

✍ Scribed by Arnold, Douglas N. ;Boffi, Daniele ;Falk, Richard S. ;Gastaldi, Lucia

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 131 KB
• Volume: 17
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/cnm.450

✦ Synopsis

Abstract

Quadrilateral finite elements are generally constructed by starting from a given finite dimensional space of polynomials V̂ on the unit reference square K̂. The elements of V̂ are then transformed by using the bilinear isomorphisms F~K~ which map K̂ to each convex quadrilateral element K. It has been recently proven that a necessary and sufficient condition for approximation of order r+1 in L^2^ and r in H^1^ is that V̂ contains the space Q~r~ of all polynomial functions of degree r separately in each variable. In this paper several numerical experiments are presented which confirm the theory. The tests are taken from various examples of applications: the Laplace operator, the Stokes problem and an eigenvalue problem arising in fluid‐structure interaction modelling. Copyright © 2001 John Wiley & Sons, Ltd.