A stable interface‐enriched formulation for immersed domains with strong enforcement of essential boundary conditions. (11th September 2019)

• Record Type: Journal Article
• Authors: van den Boom, Sanne J.; Zhang, Jian; van Keulen, Fred; Aragón, Alejandro M.
• Is Part Of: International journal for numerical methods in engineering. Volume 120:Number 10(2019)
• Page Start: 1163
• Page End: 1183
• Publication Date: 2019-09-11
• Subjects: DE‐FEM -- enriched FEM -- fictitious domain problems -- immersed boundary problems -- XFEM/GFEM; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6139
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: Generating matching meshes for finite element analysis is not always a convenient choice, for instance, in cases where the location of the boundary is not known a priori or when the boundary has a complex shape. In such cases, enriched finite element methods can be used to describe the geometric features independently from the mesh. The Discontinuity‐Enriched Finite Element Method (DE‐FEM) was recently proposed for solving problems with both weak and strong discontinuities within the computational domain. In this paper, we extend DE‐FEM to treat fictitious domain problems, where the mesh‐independent boundaries might either describe a discontinuity within the object, or the boundary of the object itself. These boundaries might be given by an explicit expression or an implicit level set. We demonstrate the main assets of DE‐FEM as an immersed method by means of a number of numerical examples; we show that the method is not only stable and optimally convergent but, most importantly, that essential boundary conditions can be prescribed strongly.