Some error estimates on the large jump asymptotic approach for the interface problem

摘要

A large jump asymptotic framework is presented for reduction of an elliptic or parabolic problem with strongly discontinuous coefficient jumps to a small number of subproblems with continuous coefficients and independent of the discontinuity amplitude by I. Klapper and T. Shaw (2007) [9]. Based on this frame, error estimates on the approximate asymptotic expansion solution in norms L2 and H1 are derived by linear finite element approximations to the corresponding subproblems whose solutions are connected with one by one when the interface is an open curve, and this connection brings the main difficulty in the error analysis. Simultaneously, as the interface is a closed curve, a feasible algorithm is designed according to the characters of the subproblems and the principle of superposition for the differential equation. Numerical experiments are carried on to verify the theoretical result and our new algorithm. Furthermore, a numerical simulation for a radiative heat transfer problem also confirms them with agreeable temperature distributions and small energy conservation error.