Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through mesh-topology modifications, constraint handling for non-matching interfaces, and repeated remeshing with state transfer. This work presents an unfitted multi-level hp-refinement strategy that enriches a fixed base discretization by independently positioned overlay meshes. The global approximation space is constructed by superposition of the active spaces across all refinement levels, while homogeneous constraints on artificial overlay boundaries ensure global $C^0$ continuity. Coupling between non-matching meshes is assembled over admissible integration regions defined by intersections of element partitions, enabling reuse of standard element-level finite element routines within a lightweight superposition framework. In contrast to fitted multi-level approaches, overlay boundaries are not required to align with underlying mesh interfaces. This reduces inter-level coupling and allows refinement zones to be inserted, translated, and removed without modifying the base discretization. Numerical studies for discontinuous and singular benchmark problems, as well as a moving source, demonstrate the performance of the method. The unfitted approach retains exponential convergence for non-smooth problems and achieves improved error-to-cost ratios compared to fitted multi-level hp-refinement. For representative cases, comparable accuracy is obtained with substantially fewer degrees of freedom, while localized high-order refinement accurately tracks moving features.

翻译：局部化特征（如奇异性、陡峭梯度、间断性及移动源）需要自适应有限元离散化。传统细化策略通过网格拓扑修改、非匹配界面的约束处理以及反复网格重构与状态传递引入显著计算开销。本文提出一种无拟合多层hp细化策略，通过独立定位的覆盖网格对固定基础离散化进行富集。全局近似空间由所有细化层级上的活动空间通过叠加构造，而人工覆盖边界上的齐次约束确保全局$C^0$连续性。非匹配网格间的耦合通过由单元划分交定义的可容许积分区域进行组装，从而在轻量级叠加框架内重用标准单元级有限元程序。与拟合多层方法不同，覆盖边界无需与底层网格界面对齐，这减少了层间耦合，并允许在不修改基础离散化的情况下插入、平移和移除细化区域。针对间断与奇异基准问题以及移动源的数值研究展示了该方法的性能。该无拟合方法对非光滑问题保持指数收敛，在误差成本比上优于拟合多层hp细化。在典型算例中，以显著更少的自由度获得相当精度，同时局部高阶细化能精确追踪移动特征。