Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes

Table 1

The errors |‖𝑢−𝑢_ℎ‖|_𝜀,ℎ/|‖𝑢‖|_𝜀,ℎ employing approximation form (12) under mesh 1.

𝜀⧵𝑚×𝑛	8×8	16×16	32×32	64×64
2^0	3.5080𝑒−001	1.8514𝑒−001	9.3821𝑒−002	4.7068𝑒−002
2^−2	3.3197𝑒−001	1.7650𝑒−001	8.9611𝑒−002	4.4977𝑒−002
2^−4	3.9897𝑒−001	2.3228𝑒−001	1.2090𝑒−001	6.1071𝑒−002
2^−6	5.7470𝑒−001	5.3768𝑒−001	3.6322𝑒−001	2.0029𝑒−001
2^−8	5.4334𝑒−001	5.7884𝑒−001	6.0446𝑒−001	5.4125𝑒−001
2^−10	5.3774𝑒−001	5.5800𝑒−001	5.6811𝑒−001	5.8575𝑒−001
Poisson	5.3734𝑒−001	5.5616𝑒−001	5.6087𝑒−001	5.6205𝑒−001
Biharmonic	4.5852𝑒−002	2.4188𝑒−002	1.2255𝑒−002	6.1481𝑒−003