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.