High order unfitted finite element methods on level set domains using isoparametric mappings

• Published in: Computer methods in applied mechanics and engineering Vol. 300; pp. 716 - 733
• Main Author: Lehrenfeld, Christoph
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2016
• Subjects: Computer simulation; Curved; Finite element method; High order methods; Integrals; Interface problems; Isoparametric finite element method; Level set; Mapping; Mathematical analysis; Mathematical models; Numerical integration; Reconstruction; Unfitted finite element method; Unfitted finite element method; Numerical integration; Level set; High order methods; Isoparametric finite element method; Interface problems
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2015.12.005

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is suitable for the case of piecewise planar interfaces is combined with a parametric mapping of the underlying mesh resulting in an isoparametric unfitted finite element method. The parametric mapping is constructed in a way such that the quality of the piecewise planar interface reconstruction is significantly improved allowing for high order accurate computations of (unfitted) domain and surface integrals. We present the method, discuss implementational aspects and present numerical examples which demonstrate the quality and potential of this method.