In this paper we present and analyze Uzawa type algorithms for solving discretized variational inequalities arising from two phase Stefan type problems. For a Uzawa type algorithm and its improved version we show convergence and derive bounds on convergence rates. For the improved Uzawa algorithm, the convergence rate is shown to be uniformly bounded away from 1 if τh−2 is kept bounded, with τ ...

Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for one dimensional material with non-local flux, expressed in terms of Caputo derivative, which derives space-fractional Stefan problem. We prove existence unique solution to fractional Neumann boundary condition at fixed face $x=0$, where domain, initial time, consists liquid solid....

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering boundary influx condition from knowledge of position moving front and initial state. derived logarithmic stability estimate that shows inversion may be severely ill-posed. The proof is based on integral equations unique continuation holomorphic functions. also proposed direct algorith...

The mathematical model of the movement of the shoreline in a sedimentary ocean basin (A Shoreline Problem) is a Stefan problem with variable latent heat. Swenson et al. [1] utilized an analogy with one-phase melting problem and developed a mathematical model for movement of shoreline in a sedimentary basin in response to changes in sediment line flux, tectonic subsidence of Earth's crust and se...