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

Table 2

The errors |‖𝑢−𝑢_ℎ‖|_𝜀,ℎ/|‖𝑢‖|_𝜀,ℎ employing approximation form (14) under mesh 1.

𝜀⧵𝑚×𝑛	8×8	16×16	32×32	64×64
2^0	3.6561𝑒−001	1.8595𝑒−001	9.3374𝑒−002	4.6737𝑒−002
2^−2	3.1147𝑒−001	1.5806𝑒−001	7.9321𝑒−002	3.9697𝑒−002
2^−4	1.4057𝑒−001	7.1356𝑒−002	3.5816𝑒−002	1.7925𝑒−002
2^−6	8.5681𝑒−002	4.4048𝑒−002	2.2146𝑒−002	1.1088𝑒−002
2^−8	8.1275𝑒−002	4.2229𝑒−002	2.1271𝑒−002	1.0642𝑒−002
2^−10	8.1006𝑒−002	4.2163𝑒−002	2.1281𝑒−002	1.0662𝑒−002
Poisson	8.0988𝑒−002	4.2159𝑒−002	2.1284𝑒−002	1.0667𝑒−002
Biharmonic	4.8120𝑒−002	2.4478𝑒−002	1.2292𝑒−002	6.1526𝑒−003