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Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics

Matteo Negri — 2014

ESAIM: Control, Optimisation and Calculus of Variations

We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence...

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method

Adrian J. LewMatteo Negri — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional ...

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method

Adrian J. LewMatteo Negri — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional ...

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