Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations

Journal of Inequalities and Applications

Table 3 The \(L^{\infty}\) error estimates at T = 0.001

k = 0	λ = 0.25		λ = 0.5		λ = 0.5		λ = 0.5
	θ = 0		θ = 0.25		θ = −0.25		θ = 0
	error	order	error	order	error	order	error	order
N = 10	6.03E−04	–	1.30E−03	–	1.02E−03	–	9.64E−04	–
N = 20	2.60E−04	1.21	6.98E−04	0.90	5.37E−04	0.93	4.78E−04	1.01
N = 40	1.21E−04	1.10	3.52E−04	0.99	2.73E−04	0.98	2.36E−04	1.02

k = 1	λ = 0.25		λ = 0.5		λ = 0.5		λ = 0.5
	θ = 0		θ = 0.25		θ = −0.25		θ = 0
	error	order	error	order	error	order	error	order
N = 10	1.67E−02	–	1.68E−02	–	1.68E−02	–	1.68E−02	–
N = 20	4.15E−03	2.01	4.15E−03	2.11	4.15E−03	2.01	4.15E−03	2.01
N = 40	1.03E−03	2.01	1.03E−03	2.01	1.03E−03	2.01	1.03E−03	2.01

k = 2	λ = 0.25		λ = 0.5		λ = 0.5		λ = 0.5
	θ = 0		θ = 0.25		θ = −0.25		θ = 0
	error	order	error	order	error	order	error	order
N = 10	9.72E−04	–	9.65E−04	–	9.72E−04	–	9.68E−04	–
N = 20	1.27E−04	2.93	1.27E−04	2.93	1.27E−04	2.93	1.27E−04	2.93
N = 40	1.61E−05	2.98	1.61E−05	2.98	1.61E−05	2.98	1.61E−05	2.98