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

Table 2

The numerical error for fm. 1 (our formulation) and fm. 2 (Arbogast's formulation).

Case	Mesh	‖𝑢−𝑢ℎ‖		‖∇⋅(𝑢−𝑢ℎ)‖		‖𝑝−𝑝ℎ‖		‖𝑃𝑠𝑝−𝑝ℎ‖
		fm. 1	fm. 2	fm. 1	fm. 2	fm. 1	fm. 2	fm. 1	fm. 2
1	4	4.90𝑒−2	5.67𝑒−2	3.06𝑒−1	3.24𝑒−1	2.93𝑒−2	2.93𝑒−2	4.53𝑒−3	4.17𝑒−3
	8	1.78𝑒−2	2.05𝑒−2	1.53𝑒−1	1.62𝑒−1	1.47𝑒−2	1.47𝑒−2	1.24𝑒−3	1.20𝑒−3
	16	6.45𝑒−3	7.37𝑒−3	7.67𝑒−2	8.13𝑒−2	7.37𝑒−3	7.37𝑒−3	3.18𝑒−4	3.15𝑒−4
	32	2.31𝑒−3	2.64𝑒−3	3.84𝑒−2	4.07𝑒−2	3.68𝑒−3	3.68𝑒−3	8.01𝑒−5	7.98𝑒−5
	64	8.25𝑒−4	9.38𝑒−4	1.92𝑒−2	2.03𝑒−2	1.84𝑒−3	1.84𝑒−3	2.01𝑒−5	2.01𝑒−5
2	4	4.70𝑒−2	5.47𝑒−2	2.99𝑒−1	3.22𝑒−1	2.95𝑒−2	2.94𝑒−2	5.42𝑒−3	4.97𝑒−3
	8	1.72𝑒−2	1.99𝑒−2	1.53𝑒−1	1.63𝑒−1	1.47𝑒−2	1.47𝑒−2	1.54𝑒−3	1.48𝑒−3
	16	6.25𝑒−3	7.19𝑒−3	7.75𝑒−2	8.27𝑒−2	7.37𝑒−3	7.37𝑒−3	4.04𝑒−4	3.98𝑒−4
	32	2.25𝑒−3	2.58𝑒−3	3.89𝑒−2	4.15𝑒−2	3.68𝑒−3	3.68𝑒−3	1.03𝑒−4	1.02𝑒−4
	64	8.08𝑒−4	9.21𝑒−4	1.95𝑒−2	2.08𝑒−2	1.84𝑒−3	1.84𝑒−3	2.59𝑒−5	2.58𝑒−5
3	4	9.65𝑒−2	1.09𝑒−1	4.14𝑒−1	4.67𝑒−1	1.49𝑒−1	1.49𝑒−1	7.39𝑒−3	6.21𝑒−3
	8	3.79𝑒−2	4.31𝑒−2	2.16𝑒−1	2.46𝑒−1	7.44𝑒−2	7.44𝑒−2	2.14𝑒−3	1.89𝑒−3
	16	1.42𝑒−2	1.62𝑒−2	1.11𝑒−1	1.28𝑒−1	3.72𝑒−2	3.72𝑒−2	5.72𝑒−4	5.19𝑒−4
	32	5.19𝑒−3	5.91𝑒−3	5.63𝑒−2	6.51𝑒−2	1.86𝑒−2	1.86𝑒−2	1.47𝑒−4	1.35𝑒−4
	64	1.87𝑒−3	2.13𝑒−3	2.84𝑒−2	3.28𝑒−2	9.31𝑒−3	9.31𝑒−3	3.72𝑒−5	3.44𝑒−5