New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow

Table 1

The comparison of maximum absolute error, maximum relative error, and 𝐿² error when Δ𝑡=ℎ.

The step size in space	ℎ=1/4	ℎ=1/8	ℎ=1/16	ℎ=1/32
max𝐸𝐶	3.9203𝑒−3	1.0783𝑒−3	2.7107𝑒−4	6.8318𝑒−5
max𝑅𝐶	2.0388𝑒−2	5.1581𝑒−3	9.8663𝑒−3	2.5216𝑒−3
||𝐶−𝑈||	2.1257𝑒−3	5.4288𝑒−4	1.3603𝑒−4	3.4020𝑒−5
max𝐸𝐶/ℎ^2	0.06273	0.06902	0.06939	0.06996
||𝐶−𝑈||/ℎ^2	0.03401	0.03474	0.03483	0.03484