Geometrically Unfitted Finite Element Methods and Applications (eBook)

Proceedings of the UCL Workshop 2016

Stéphane P. A. Bordas, Erik Burman, Mats G. Larson, Maxim A. Olshanskii (Herausgeber)

eBook Download: PDF

2018 | 1st ed. 2017
XIII, 361 Seiten
Springer International Publishing (Verlag)
978-3-319-71431-8 (ISBN)

Infos

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.

Inhalt

Introduction.- 1 Deriving robust unfitted finite element methods from augmented Lagrangian formulations (E. Burman, P. Hansbo).- 2 Cut finite element methods for linear elasticity problems (P. Hansbo, M.G. Larson, K. Larsson).- 3 A higher order isoparametric fictitious domain method for level set domains (C. Lehrenfeld).- 4 An overview of recent results on Nitsches method for contact problems (F. Chouly, M. Fabre, P. Hild, R. Mlika, J. Pousin, Y. Renard).- 5 Inf-sup stable unfitted extended finite element methods with Lagrange multipliers for the Stokes equations (M. Fournié, A. Lozinski).- 6 Penalty-free Nitsches method for interface problems (T. Boiveau, E. Burman, S. Claus).- 7 Trace Finite Element Methods for PDEs on Surfaces (M. A. Olshanskii, A. Reusken).- 8 A Cut Discontinuous Galerkin Method for Coupled Bulk-Surface Problems (A. Massing).- 9 A space-time cut finite element method for convection-diffusion problems in time dependent domains (S. Zahedi).- 10 Well Conditioned Extended Finite Elements and Vector Level Sets for Three-Dimensional Crack Propagation (S. Bordas, A. Kostas).- 11 Unfitted FEM for modelling the interaction of multiple fractures in a poroelastic medium (B. Giovanardi, L. Formaggia, A. Scotti, P. Zunino).

Produkt-Details

• Erscheint lt. Verlag: 13.3.2018
• Reihe/Serie: Lecture Notes in Computational Science and Engineering
• Reihe/Serie: Lecture Notes in Computational Science and Engineering
• Zusatzinfo: XIII, 361 p.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: augmented Lagrangian techniques • Contact Problems • Crack propagation • cutFEM • Discontinuous Galerkin method • Extended Finite Element Methods • fictitious domain methods • finite element methods for PDEs on surfaces • flow in poroelastic media • Flow in Porous Media • geometrically unfitted finite element methods • geometrically unfitted finite element methods applications • ghost penalty • Incompressible Flow • Lagrange multiplier methods • linear elasticity problems • MSC 2010: 65N12, 65N15, 65N85, 65N30, 74G15, 74S05, 74M15 • Nitsche’s method for interfaces and boundaries • traceFEM
• ISBN-10: 3-319-71431-7 / 3319714317
• ISBN-13: 978-3-319-71431-8 / 9783319714318