A Class of Spectral Element Methods and Its A Priori/A Posteriori Error Estimates for 2nd-Order Elliptic Eigenvalue Problems

Table 1

Errors of LGL-SM, modal, and Eq-SM for 1st eigenvalue.

𝑁	DOF	LGL-SM	Modal-SM	Eq-SM
		𝜆1	𝜆1	𝜆1
4	9	5.19𝐸+00	5.19𝐸+00	5.19𝐸+00
5	16	4.51𝐸−01	4.51𝐸−01	4.51𝐸−01
6	25	7.68𝐸−03	7.68𝐸−03	7.68𝐸−03
7	36	1.07𝐸−05	1.07𝐸−05	1.07𝐸−05
8	49	1.21𝐸−05	1.21𝐸−05	1.21𝐸−05
9	64	9.16𝐸−07	9.16𝐸−07	9.16𝐸−07
10	81	2.46𝐸−08	2.46𝐸−08	2.48𝐸−08
11	100	2.91𝐸−10	2.91𝐸−10	4.35𝐸−09
12	121	9.31𝐸−13	1.06𝐸−12	2.79𝐸−08
13	144	5.68𝐸−14	1.28𝐸−13	1.41𝐸−07
14	169	2.84𝐸−14	1.28𝐸−13	2.28𝐸−06
15	196	7.82𝐸−14	2.13𝐸−14	3.60𝐸−05