Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex domains, where the regularity assumption holds for Stokes equation, the approximation to the curl of the true solution has quadratic order of convergence and first order for the energy norm. If the solution shows singularity, a posterior error estimator is developed and a separate marking adaptive finite element procedure is proposed, together with its convergence proved. Both a priori and a posteriori error analysis are supported by the numerical examples.

翻译：本文研究了与四曲线问题脱钩配方的精度元素近似近似于四曲线问题。 构建与四曲线问题某种一致元素的困难已经大大减少。 对于Convex 域, 其常态假设适用于斯托克斯方程式, 与真正解决方案曲线的近似性具有二次交汇和能源规范第一顺序。 如果解决方案显示单一性, 将开发一个后误差估计器, 并提议一个单独的标记适应性有限元素程序, 并证明其趋同性。 数字示例支持先验和事后误差分析。