Convergence of a Crank-Nicolson difference scheme for heat equations with interface in the heat flow and concentrated heat capacity
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 the 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 L2 norm.
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