An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain

A finite difference scheme for the heat equation with mixed boundary conditions on a moving domain is presented. We use an immersed interface technique to discretize the Neumann condition and the Shortley–Weller approximation for the Dirichlet condition. Monotonicity of the discretized parabolic operator is established. Numerical results illustrate the feasibility of the approach.