A Rectangular Mixed Finite Element Method with a Continuous Flux for an Elliptic Equation Modelling Darcy Flow

Table 4

Numerical error and convergence rate (Δ𝑡=𝐶ℎ).

Mesh	5×5		10×10		20×20		40×40
Norm type	Error	Rate	Error	Rate	Error	Rate	Error	Rate
‖𝑢‖𝑙^2(𝐿^2)	1.83𝑒−4	—	7.10𝑒−5	1.36	3.38𝑒−5	1.07	1.65𝑒−5	1.03
‖𝑢‖𝑙^∞(𝐿^2)	1.29𝑒−2	—	5.19𝑒−3	1.31	2.64𝑒−3	0.97	1.37𝑒−3	0.95
𝑝𝑙^2(𝐿2)	1.33𝑒−3	—	6.67𝑒−4	1.00	3.33𝑒−4	1.00	1.67𝑒−4	1.00
𝑝𝑙^∞(𝐿2)	9.43𝑒−2	—	4.71𝑒−2	1.00	2.35𝑒−2	1.00	1.18𝑒−2	1.00
‖𝐶‖𝑙^2(𝐻^1)	2.32𝑒−3	—	1.16𝑒−3	1.01	5.78𝑒−4	1.00	2.88𝑒−4	1.00
‖𝐶‖𝑙^∞(𝐻^1)	1.63𝑒−1	—	8.18𝑒−2	1.00	4.11𝑒−2	0.99	2.05𝑒−2	0.99