Geometrically Unfitted Finite Element Methods and Applications

Description

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering. Front Matter ....Pages i-xiii Deriving Robust Unfitted Finite Element Methods from Augmented Lagrangian Formulations (Erik Burman, Peter Hansbo)....Pages 1-24 Cut Finite Element Methods for Linear Elasticity Problems (Peter Hansbo, Mats G. Larson, Karl Larsson)....Pages 25-63 A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains (Christoph Lehrenfeld)....Pages 65-92 An Overview of Recent Results on Nitsche’s Method for Contact Problems (Franz Chouly, Mathieu Fabre, Patrick Hild, Rabii Mlika, Jérôme Pousin, Yves Renard)....Pages 93-141 Stability and Optimal Convergence of Unfitted Extended Finite Element Methods with Lagrange Multipliers for the Stokes Equations (Michel Fournié, Alexei Lozinski)....Pages 143-182 Penalty-Free Nitsche Method for Interface Problems (Thomas Boiveau, Erik Burman, Susanne Claus)....Pages 183-210 Trace Finite Element Methods for PDEs on Surfaces (Maxim A. Olshanskii, Arnold Reusken)....Pages 211-258 A Cut Discontinuous Galerkin Method for Coupled Bulk-Surface Problems (André Massing)....Pages 259-279 A Space-Time Cut Finite Element Method with Quadrature in Time (Sara Zahedi)....Pages 281-306 Well Conditioned Extended Finite Elements and Vector Level Sets for Three-Dimensional Crack Propagation (Konstantinos Agathos, Giulio Ventura, Eleni Chatzi, Stéphane P. A. Bordas)....Pages 307-329 Unfitted FEM for Modelling the Interaction of Multiple Fractures in a Poroelastic Medium (Bianca Giovanardi, Luca Formaggia, Anna Scotti, Paolo Zunino)....Pages 331-352 Back Matter ....Pages 353-361