L2hforadaptivity Ef F1 F3 F5 -

For Poisson’s equation with a sharp interior layer (e.g., f5‑dominant region), pure L² adaptivity refines too late, while H¹‑only refines the entire layer uniformly. The combination:

The triplet (f1, f3, f5) under L²‑H¹ adaptivity provides a robust, practical error control for elliptic problems. Implementations are available in open‑source FEM libraries (e.g., deal.II, FEniCS, MFEM) under the “dual‑norm” or “goal‑oriented” modules. l2hforadaptivity ef f1 f3 f5