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Table 2 \(\pmb{L^{\infty}}\) -errors, the number of iterations, and the CPU for linear obstacle problem with \(\pmb{\varphi _{2}}\) ( 5.4 )

From: Accurate and efficient numerical solutions for elliptic obstacle problems

\(\boldsymbol{(\varepsilon =10^{-6})}\)

PDL1P

Obstacle SOR

Resolution

\(\boldsymbol{L^{\infty}}\) -error

Iter (CPU)

\(\boldsymbol{L^{\infty}}\) -error

Iter (CPU)

32 × 32

8.91⋅10−3

715 (0.09)

8.69⋅10−3

62 (0.02)

64 × 64

3.01⋅10−3

1,340 (0.60)

3.05⋅10−3

122 (0.04)

128 × 128

7.66⋅10−4

1,971 (3.51)

7.64⋅10−4

244 (0.22)

256 × 256

1.86⋅10−4

2,072 (14.85)

1.88⋅10−4

489 (1.63)

  1. The PDL1P uses the parameters suggested in [14] (μ = 0.1, \(r_{1}=0.008\), \(r_{2}=15.625\)).