The fictitious domain method with penalty for the parabolic problem in moving-boundary domain: The error estimate of penalty and the finite element approximation

摘要

We consider the fictitious domain method with penalty for the parabolic problem in a moving-boundary domain. Two types of penalty (the H~1 and L~2-penalty methods) are investigated, for which we obtain the error estimate of penalty. Moreover, for H~1-penalty method, the H~2-regularity and a-priori estimate depending on the penalty parameter e are obtained. We apply the finite element method to the H~1-penalty problem, and obtain the stability and error estimate for the numerical solution. The theoretical results are confirmed by the numerical experiments.