An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions

An immersed finite volume element method is developed to solve 2D elliptic interface problems with a variable coefficient that has a finite jump across an interface. The solution and the flux may also have a finite jump across the interface. Using the source removal technique, an equivalent elliptic interface problem with homogeneous jump conditions is obtained. The nodal basis functions are constructed to satisfy the homogeneous jump conditions near the interface and the usual finite element nodal basis functions are applied away from the interface. The resulting linear problem is simple and easy to solve. A proof of the error estimate in the energy norm is given. Numerical experiments demonstrate the convergence rates of the proposed method with the usual O(h2)O(h2) in the L2L2, the L∞L∞ norms, and O(h)O(h) in the H1H1 norm.