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...
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
...
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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