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

  • Ilia Braianov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1196)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akrivis, G.D., Dougalis, V.A.: Finite difference discretizations of Some initial and boundary value problems with interface. Math. Comp. 56 (1991) 505–522Google Scholar
  2. 2.
    Samarskii, A.A.: Introduction in difference scheme theory. Nauka, Moscow 1971 (Russian)Google Scholar
  3. 3.
    Samarskii, A.A.: Theory of difference schemes. Nauka, Moscow 1977 (Russian)Google Scholar
  4. 4.
    Thomée, V.: Galerkin finite element methods for parabolic problems. Lecture notes in Math. 1054, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1984Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ilia Braianov
    • 1
  1. 1.Center of Applied Mathematics and InformaticsUniversity of RousseRousseBulgaria

Personalised recommendations