Higher‐order conformal decomposition finite element method. Issue 1 (25th October 2016)

• Record Type: Journal Article
• Authors: Omerović, Samir; Fries, Thomas‐Peter
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 855
• Page End: 856
• Publication Date: 2016-10-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610416
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Numerical simulations of structures using higher‐order finite elements is still a challenging task, in particular for domains with curved boundaries. A new higher‐order accurate approach is proposed, combining the advantages of the classical p ‐FEM with embedded domain methods. Boundaries and/or interfaces are described implicitly using the level set method. In the elements cut by the zero level set, an automatic decomposition into interface aligned, i. e. conforming sub‐elements is realized. Transfinite mappings are utilized to construct higher‐order sub‐elements by mappings of reference elements to the two sides of the boundary or interface. It is shown that although the resulting sub‐elements are not always well‐shaped, optimal convergence rates are possible. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)