A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

Table 1

Errors and order of convergence.

(ℎ,Δ𝑡)	‖𝑢−𝑢ℎ‖𝐿∞(𝐿2(Ω))	Order	‖𝑢−𝑢ℎ‖𝐿∞(𝐻1(Ω))	Order
(√2/8,1/16)	1.4059𝑒−003	—	1.8754𝑒−002	—
(√2/16,1/32)	3.6420𝑒−004	1.9486	9.6596𝑒−003	0.9572
(√2/32,1/64)	9.2569𝑒−005	1.9761	4.9011𝑒−003	0.9789
(ℎ,Δ𝑡)	𝜆−𝜆ℎ𝐿∞((𝐿2(Ω))^2)	Order	𝜎−𝜎ℎ𝐿∞((𝐿2(Ω))^2)	Order
(√2/8,1/16)	1.8701𝑒−002	—	9.7089𝑒−003	—
(√2/16,1/32)	9.6528𝑒−003	0.9541	5.1777𝑒−003	0.9070
(√2/32,1/64)	4.9003𝑒−003	0.9781	2.6722𝑒−003	0.9543