Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis

Immersed finite element (IFE) methods are a group of long-existing numerical for solving interface problems on unfitted meshes. A core argument the is to avoid mesh regeneration procedure when moving problems. Despite various applications in problems, complete theoretical study convergence behavior still missing. This research devoted closing gap between experiments and theory. We present first fully discrete analysis including stability optimal error estimates backward Euler IFE method parabolic Numerical results also presented validate analysis.