An adaptive edge element method is designed to approximate a quasilinear [Formula: see text]-elliptic problem in magnetism, based on a residual-type a posteriori error estimator and general marking strategies. The error estimator is shown to be both reliable and efficient, and its resulting sequence of adaptively generated solutions converges strongly to the exact solution of the original quasilinear system. Numerical experiments are provided to verify the validity of the theoretical results.

中文翻译：

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拟线性 H(curl)-椭圆问题的自适应边缘元素逼近

基于残差型后验误差估计器和一般标记策略，设计了一种自适应边缘元素方法来逼近磁性中的拟线性[公式：见文本]-椭圆问题。误差估计器被证明是可靠和有效的，其自适应生成的解的结果序列强烈地收敛于原始准线性系统的精确解。提供了数值实验来验证理论结果的有效性。