Convergence of a Crank-Nicolson Difference Scheme for Heat Equations with Interface in the Heat Flow and Concentrated Heat Capacity

摘要

In this paper we consider initial value problems for heat equation with discontinuous heat flow and concentrated heat capacity in interior points or at the boundary. Convergence of the Crank-Nicolson scheme is analyzed via teh concept of elliptic projection. Namely second order convergence is proved for the corresponding elliptic problems in special norms. Then, splitting the error of the heat problem into two errors we prove second order estimates in space and time in modified L_2 norm.