Efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions
Journal article, 2013

In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes. Examples of such methods are the fictitious domain method, the extended finite element method, and Nitsche's method. In all these methods, integrals must be computed over cut cells or subsimplices, which is challenging to implement, especially in three space dimensions. In this note, we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices. As a canonical example of an overlapping mesh method, we consider Nitsche's method, which we apply to Poisson's equation and a linear elastic problem. © 2013 Society for Industrial and Applied Mathematics.

Non-matching mesh

Immersed interface

Overlapping mesh


Discontinuous Galerkin method

Computational geometry


Nitsche method

Extended finite element method


A. Massing

M. G. Larson

Anders Logg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 35 1 C23-C47

Subject Categories


Computational Mathematics



More information