A Family of Two-Grid Partially Penalized Immersed Finite Element Methods for Semi-linear Parabolic Interface Problems

In this paper, we present a family of two-grid algorithms for semi-linear parabolic interface problems based on Partially penalized immersed finite element discretizations. Optimal a priori error estimates are derived both in the energy norm and $$L^2$$ norm, under the standard piecewise $$H^2$$ regularity assumption for the exact solution. For the nonlinear right hand side, we investigate two-grid methods base on Newton method. The efficiency of the two-grid methods is confirmed theoretically and numerically.