Many names of the Trefftz method. (November 2018)

• Record Type: Journal Article
• Authors: Kołodziej, Jan Adam; Grabski, Jakub Krzysztof
• Is Part Of: Engineering analysis with boundary elements. Volume 96(2018)
• Page Start: 169
• Page End: 178
• Publication Date: 2018-11
• Subjects: Boundary value problems -- Trefftz method -- Boundary methods; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2018.08.013
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The Trefftz method is understood as an approximate method for solving boundary value problems in which the approximate solution is a linear combination of trial functions satisfying exactly the governing equation. The method was proposed by Erich Trefftz in Zürich in 1926 as an alternative to the Ritz method in which the boundary conditions are satisfied exactly. However such an approach was applied already in some previous papers. There are also examples in the publications published after 1926 in which the authors used this approach however they did not mention the name " Trefftz method ". There are also different modifications of the Trefftz-type methods in which the authors proposed new names because of these modifications. The aim of this paper is to present many variations of the Trefftz method and to collect the names under which they were published, before the original paper of Erich Trefftz in 1926 and after it.