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Higher order Trefftz‐like Finite Element Method on meshes with L‐shaped elements
Author(s) -
Weißer Steffen
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410009
Subject(s) - polygon mesh , finite element method , discretization , basis function , mathematics , basis (linear algebra) , sequence (biology) , boundary value problem , regular polygon , boundary element method , mathematical analysis , geometry , structural engineering , engineering , biology , genetics
In 2009, the BEM‐based FEM was introduced as an numerical approach for the treatment of boundary value problems. It is a Finite Element Method (FEM) that uses Trefftz‐like basis functions which are defined to fulfil the underlying differential equation locally and which are treated by means of Boundary Element Methods (BEM). Due to the implicit definition of basis functions, this approach is applicable on general polygonal and polyhedral meshes and yields conforming approximations. The elements of the discretization do not necessarily have to be convex. After a review of the recent development of higher order basis functions the method is applied to a model problem on a sequence of meshes with L‐shaped elements. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)