An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump

We study an adaptive immersed finite element method for solving parabolic interface problems with nonzero flux jump in a two-dimensional convex polygonal domain. We use unfitted finite element meshes to discretize the spatial domain where the grid points do not need to fit the interface. New error indicators are introduced to control the error due to unfitted meshes. We derive a global upper bound as well as a local lower bound for the error using energy method. An adaptive algorithm for immersed finite element method is provided using the error indicators. Numerical experiment is presented to demonstrate the behavior of the adaptive algorithm for the proposed method.