Failures of local approximation in finite-element methods

✍ Scribed by Douglas A. Kurtze

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 1021 KB
• Volume: 23
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620230806

✦ Synopsis

It is shown that standard finite-element discretizations of second-order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite-element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is discussed.