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.

我们研究了一种自适应浸入式有限元方法，用于解决二维凸多边形域中具有非零通量跳跃的抛物线界面问题。我们使用未拟合的有限元网格来离散化网格点不需要拟合界面的空间域。引入了新的错误指示器来控制由于未拟合网格引起的错误。我们使用能量方法推导出误差的全局上限和局部下限。使用误差指示器提供了一种用于浸入式有限元法的自适应算法。提出了数值实验来证明所提出方法的自适应算法的行为。