We consider an adaptive finite element method for solving parabolic interface problems with nonzero flux jumps in a two-dimensional convex polygonal domain. We use continuous, piecewise linear functions for the approximation of the spatial variable whereas the backward Euler method is employed for the time discretization. The reliability bound of the estimator is derived in terms of the error indicators using the energy argument. An efficiency bound for the local error in terms of the space error indicator is also established. We provide an adaptive algorithm which reduces the error indicators below any given tolerance within a finite number of steps. Our numerical experiment reveals the performance of the derived error indicators with satisfactory numerical results.

我们考虑一种自适应有限元方法，用于解决二维凸多边形区域中非零磁通跳跃的抛物线界面问题。我们使用连续的分段线性函数来逼近空间变量，而将后向Euler方法用于时间离散化。估计器的可靠性范围是使用能量参数根据误差指标得出的。还建立了根据空间误差指示器来限制局部误差的效率。我们提供了一种自适应算法，可以在有限的步骤中将误差指标降低到任意给定的公差以下。我们的数值实验揭示了令人满意的数值结果所导出的误差指标的性能。