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Penalty-free Nitsche method for interface problems in computational mechanics

Boiveau, TBV; (2016) Penalty-free Nitsche method for interface problems in computational mechanics. Doctoral thesis , UCL (University College London). Green open access

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Abstract

Nitsche’s method is a penalty-based method to enforce weakly the boundary conditions in the finite element method. In this thesis, we consider a penalty-free version of Nitsche’s method, we prove its stability and convergence in various frameworks. The idea of the penalty-free method comes from the nonsymmetric version of the Nitsche’s method where the penalty parameter has been set to zero; it can be seen as a Lagrange multiplier method, where the Lagrange multiplier has been replaced by the boundary fluxes of the discrete elliptic operator. The main observation is that although coercivity fails, inf-sup stability can be proven. The study focuses on compressible and incompressible elasticity. An unfitted framework is considered when the computational mesh does not fit with the physical domain (fictitious domain method). The penalty-free Nitsche’s method is also used to enforce the coupling for interface problems when the mesh fits the interface (nonconforming domain decomposition) or not (unfitted domain decomposition). Fluid structure interaction is also investigated, a new fully discrete implicit scheme is introduced.

Type: Thesis (Doctoral)
Title: Penalty-free Nitsche method for interface problems in computational mechanics
Event: University College London
Open access status: An open access version is available from UCL Discovery
Language: English
Keywords: Nitsche's method, Finite elements, Boundary imposition, Interface coupling, Domain decomposition, Fictitious domain, Cut Finite Element Method, Fluid-structure interaction
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/1503355
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