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In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For the resulting systems we discuss three iterative methods and give sufficient conditions for convergence.

The main goal of this paper is to address the numerical solution of a wave equation with discontinuous coefficients by a finite element method using domain decomposition and semimatching grids. A wave equation with absorbing boundary conditions is considered, the coefficients in the equation essentially differ in the subdomains. The problem is approximated by an explicit in time finite difference scheme combined with a piecewise linear finite element method in the space variables on a semimatching grid. The matching condition on the interface is taken into account by means of Lagrange multipliers. The resulting system of linear equations of the saddle-point form is solved by a conjugate gradient method.

This paper deals with a time-domain mathematical model for a linearized acoustics problem in the presence of an uniform flow. First, the resulting initial-boundary value problem is rewritten in a suitable functional framework; then a time discretization is proposed. Finally stability and error estimates are stated.

The subject under study is an open subsystem of a larger linear and conservative system and the way in which it is coupled to the rest of system. Examples are a model of crystalline solid as a lattice of coupled oscillators with a finite piece constituting the subsystem, and an open system such as the Helmholtz resonator as a subsystem of a larger conservative oscillatory system. Taking the view of an observer accessing only the open subsystem we ask, in particular, what information about the entire system can be reconstructed having such limited access. Based on the unique minimal conservative extension of an open subsystem, we construct a canonical decomposition of the conservative system describing, in particular, its parts coupled to and completely decoupled from the open subsystem. The coupled one together with the open system constitute the unique minimal conservative extension. Combining this with an analysis of the spectral multiplicity, we show, for the lattice model in particular, that .