Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema

Table 1

Left: M-SL-FV WENO 5 scheme, right: M-C-SL-FD WENO 5 scheme for Example 1 on a uniform mesh of 𝑁 cells at 𝑡=0.5, CFL = 5.9, and 𝜀=10⁻⁴⁰.

𝑁	M-SL-FV WENO 5				M-C-SL-FD WENO 5
	𝐿^1 error	Order	𝐿^∞ error	Order	𝐿^1 error	Order	𝐿^∞ error	Order
10	1.00𝐸−02	—	2.03𝐸−02	—	7.79𝐸−03	—	2.45𝐸−02	—
20	4.66𝐸−04	4.42	1.43𝐸−03	3.83	3.76𝐸−04	4.37	1.30𝐸−03	4.24
40	1.72𝐸−05	4.76	5.25𝐸−05	4.77	9.46𝐸−06	5.31	3.72𝐸−05	5.13
80	5.68𝐸−07	4.92	1.62𝐸−06	5.02	3.17𝐸−07	4.90	1.15𝐸−06	5.02
160	1.78𝐸−08	5.00	5.09𝐸−08	4.99	9.32𝐸−09	5.09	3.25𝐸−08	5.15