Fictitious domain finite element methods using cut elements

By Erik Burman, Peter Hansbo. 2012

516 citations recorded by the source corpus.

We extend the classical Nitsche type weak boundary conditions to a fictitious domain setting. An additional penalty term, acting on the jumps of the gradients over element faces in the interface zone, is added to ensure that the conditioning of the matrix is independent of how the boundary cuts the mesh. Optimal a priori error estimates in the H1- and L2-norms are proved as well as an upper bound on the condition number of the system matrix.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/2dc753090d37e5ffdf7fd88a8eda47f9b099b596

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Dominik Schillinger
2. Martin Ruess
3. Alexander Düster
4. Ernst Rank
5. Thomas J. R. Hughes
6. Yuri Bazilevs
7. Erik Burman
8. Nils Zander

In Computational Theory and Mathematics

1. Dominik Schillinger
2. Martin Ruess
3. Alexander Düster
4. Yuri Bazilevs
5. Ernst Rank
6. Erik Burman
7. Mats G. Larson
8. Nils Zander

In Electrical and Electronic Engineering

1. Dominik Schillinger
2. Martin Ruess
3. Erik Burman
4. Peter Hansbo
5. Gunilla Kreiss
6. Eddie Wadbro
7. Sara Zahedi
8. Martin Berggren

Citations in the corpus

• The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “The most popular approaches include the penalty method [8, 9, 55, 199], the Lagrange multiplier method [29, 55, 56, 58, 59, 61], and Nitsche’s method [17, 30, 43, 51, 64, 66, 147, 171].”
• Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The fictitious domain approach has been widely used in conjunction with penalty methods [12, 13], the mortar approach [14], Lagrange multipliers [11, 15–18], Nitsche’s method [19], extended finite elements [20–23], discontinuous Galerkin [24] and spectral methods [25–27] to address problems of struc”
• CutFEM: Discretizing geometry and partial differential equations (2015, methodology): “For cases such as this, a useful trick [12, 27] is to add a penalty term in the interface zone that extends the coercivity to the whole mesh domain, that is, in the O.”
• A uniformly well-conditioned, unfitted Nitsche method for interface problems (2013, methodology): “Here we consider the same two-dimensional boundary-value problem as studied by Hansbo and Hansbo [9].”