Abstract We present and analyze an adaptive finite element method for a semilinear parabolic interface problem subject to nonzero flux jump in a two-dimensional bounded convex polygonal domain. The residual-based a posteriori error estimates are derived using energy argument. Our strategy is to avoid solving the nonlinear system by considering a linearized fully discrete scheme. An adaptive algorithm is constructed using the derived error estimators. A global upper bound for the error is derived which is bounded by the element residual and interior jump residual, whereas a local lower bound in terms of the space error indicator is established. The theory presented is complemented by numerical experiments to illustrate the proposed algorithm.

中文翻译：

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具有非零通量跳跃的半线性抛物线界面问题的自适应有限元方法

摘要 我们提出并分析了二维有界凸多边形域中受非零通量跳跃影响的半线性抛物线界面问题的自适应有限元方法。使用能量参数导出基于残差的后验误差估计。我们的策略是通过考虑线性化完全离散方案来避免求解非线性系统。使用导出的误差估计量构建自适应算法。推导出误差的全局上限，该上限以元素残差和内部跳跃残差为界，而根据空间误差指标建立局部下限。提出的理论由数值实验补充以说明所提出的算法。