High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

Table 1

Maximum absolute error and convergence rate of the CDS and the FOC scheme with Re=100 for Problem 1.

	CDS				FOC
	Num	CPU	Error	Rate	Num	CPU	Error	Rate
1/8	6	0.000	2.57(-3)		7	0.000	3.69(-4)
1/16	8	0.000	6.41(-4)	2.00	8	0.000	2.31(-5)	4.00
1/32	10	0.032	1.61(-4)	1.99	9	0.047	1.43(-6)	4.01
1/64	11	0.140	4.03(-5)	2.00	9	0.156	8.94(-8)	4.00
1/128	11	0.360	1.01(-5)	2.00	9	0.406	5.60(-9)	4.00
1/256	10	1.203	2.52(-6)	2.00	9	1.422	3.50(-10)	4.00

Note: 2.57(-3) = 2.57 × 10⁻³, etc.