Immersed-Boundary Level Set Approach for Numerical Solution of Elliptic Interface Problems

In this paper we consider elliptic problems with variable discontinuous coefficients and interface jump conditions, in which the solution is continuous, but the jump of the flux depends on the solution. A new numerical method, based on immersed-boundary approach combined with level set method, is developed. Using regular grids it is robust and easy to implement for curvelinear interface problems. Numerical experiments are presented.