A coupled multivalued model for ice streams and its numerical simulation

Existence of weak solutions to a system of nonlinear partial differential equations modelling ice streams

“…In fact, the main result of the paper which is stated in Section 3 concerns the existence of a bounded weak solution (b.w.s) to the multivalued model. This result justifies, theoretically, the numerical treatment of the model carried out in [6], where a finite element algorithm combined with a duality technique were employed in order to cope with the free boundary nature of the model. The uniqueness of b.w.s result appears in [17], where existence was assumed.…”

“…Results obtained for the ice velocity in[6], where a numerical resolution of the model studied in this paper, is presented. The main flow takes place in the direction parallel to the t-axis.…”

Uniqueness and Collapse of Solution for a Mathematical Model With Nonlocal Terms Arising in Glaciology

“…The solution Q may present a loss of regularity at the free boundary, as recent numerical experiments shows (see Muñoz et el [17] and Calvo et al [5]). …”

Mathematical Analysis and Numerical Simulation in Magnetic Recording

“…We shall follow the ideas of [1,2], and apply a finite element method together with a duality algorithm handling Yosida approximation tools for maximal monotone operators. These techniques have already been successfully used for example in [7] and [8]. To be precise, we are going to deal with the following complementarity formulation of the problem (2.8)-(2.9) in terms of h:…”

“…where E denotes a standard finite element interval and T ∆x a uniform grid with step ∆x (we follow a similar notation to the one used in [8]).…”