Stefan Problem through Extended Finite Elements: Review and Further Investigations

Stefan Problem through Extended Finite Elements: Review and Further Investigations

A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments f...

Nonlinear Two-Phase Stefan Problem

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

A Stochastic Stefan Problem

We consider a stochastic perturbation of the Stefan problem. The noise is Brownian in time and smoothly correlated in space. We prove existence and uniqueness and characterize the domain of existence.

Nonconforming Finite Elements for the Stokes Problem

A new stability result is obtained for the approximation of the stationary Stokes problem by nonconforming piecewise cubic approximations to the velocities and a discontinuous piecewise quadratic approximation to the pressure. The basic result is that for most reasonable meshes, these elements form a stable pair without the addition of quartic bubble functions (which had previously been added t...

An Inverse Stefan Problem