A General Error Estimate For Parabolic Variational Inequalities

The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the GDM to establish a first general error estimate for numerical approximations of parabolic obstacle problems. This gives the convergence rates of several well--known conforming and non conforming numerical methods. Numerical experiments based on the hybrid finite volume method are provided to verify the theoretical results

An Adaptive Method for the Stefan Problem and its Application to Endoglacial Conduits

This paper concerns an adaptive finite element method for the Stefan one-phase problem. We derive a parabolic variational inequality using the Duvaut transformation [1]. In each time-step we consider an adaptive algorithm based on a combination of the Uzawa method associated with the corresponding multivalued operator and a convergent adaptive method for the linear problem. We justify the convergence of the method. As an application we model an endoglacial conduit in which a phase change phenomenon takes place