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The matched interface and boundary (MIB) method has a proven ability fordelivering the second order accuracy in handling elliptic interface problemswith arbitrarily complex interface geometries. However, its collocationformulation requires relatively high solution regularity. Finite volume method(FVM) has its merit in dealing with conservation law problems and its integralformulation works well with relatively low solution regularity. We propose anMIB-FVM to take the advantages of both MIB and FVM for solving ellipticinterface problems. We construct the proposed method on Cartesian meshes withvertex-centered control volumes. A large number of numerical experiments aredesigned to validate the present method in both two dimensional (2D) and threedimensional (3D) domains. It is found that the proposed MIB-FVM achieves thesecond order convergence for elliptic interface problems with complex interfacegeometries in both $L_{\infty}$ and $L_2$ norms.

Finite Volume Formulation of the MIB Method for Elliptic Interface Problems