On finite volume discretization of interface problems 
with piecewise constant coefficients

Oleg Iliev

New finite volume discretizations of interface 
problems with piecewise constant coefficients are 
presented and discussed. Standard conditions for
continuity of the solution and the normal component 
of its flux through the interfaces are considered.
The cases of continuous and discontinuous
right hand side are discussed. 
The schemes are derived under the assumption that the 
interfaces are aligned with the finite volumes surfaces. 
Different schemes are derived under different smoothness 
assumptions.  Second order 
convergence in $W_2^1$, or 
pointwise second order convergence is proved for some 
of the schemes under different smoothness assumptions.
Results from numerical experiments are presented in
order to demonstrate advanatges of the new schemes.