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

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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parameter has been set to zero; it can be seen as a Lagrange multiplier method, where the Lagrange multiplier has been replaced by the boundary fluxes of the discrete elliptic operator.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.

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