Asymptotic analysis of a metallostatic pressure type boundary condition modelled by a fictitious domain method in an aluminium casting

In this paper we present an asymptotic analysis of the treatment of a metallostatic pressure boundary condition arising from the thermomechanical modelling of aluminium castings by means of a fictitious domain method depending on a small real parameter. We introduce an asymptotic expansion for the solution of the extended problem and we prove that the leading term of such expansion is the solution of the initial problem.