Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
Citation:
Preprint
Series/Report no.:
1998;2
Abstract:
The paper presents a proof of 2nd order pointwise convergence for a new finite difference scheme for elliptic problems with discontinuous coefficients (so called interface problems). Cell-centred grid is exploited, i.e., the computational domain is divided into grid cells, and the values of the unknown function are related to the cell centers. It is assumed that the diffusivity coefficient is a constant within any grid cell, and that interfaces are aligned with the boundaries of the grid cells. The 2nd order pointwise convergence is proved under the assumption that the normal components of the fluxes of the solution are smooth enough at the midpoints of the finite volumes sides. Numerical experiments, confirming 2nd order pointwise convergence for the new scheme, are presented.
