Table 6 \(\pmb{L^{\infty}}\) and \(\pmb{L^{2}}\) error comparisons for the suggested post-process, applied to the linear problem with \(\pmb{\varphi =\varphi _{2}}\)
From: Accurate and efficient numerical solutions for elliptic obstacle problems
\(\boldsymbol{(\varepsilon=10^{-7})}\) | PDL1P | Obstacle SOR | Obstacle SOR+PP | |||
|---|---|---|---|---|---|---|
Resolution | \(\boldsymbol{L^{\infty}}\) error | \(\boldsymbol{L^{2}}\) error | \(\boldsymbol{L^{\infty}}\) error | \(\boldsymbol{L^{2}}\) error | \(\boldsymbol{L^{\infty}}\) error | \(\boldsymbol{L^{2}}\) error |
25 × 25 | 1.94⋅10−2 | 4.35⋅10−3 | 1.94⋅10−2 | 4.38⋅10−3 | 8.44⋅10−4 | 2.80⋅10−4 |
50 × 50 | 4.38⋅10−3 | 8.10⋅10−4 | 4.39⋅10−3 | 8.41⋅10−4 | 2.01⋅10−4 | 6.93⋅10−5 |
100 × 100 | 1.25⋅10−3 | 2.73⋅10−4 | 1.25⋅10−3 | 2.87⋅10−4 | 5.16⋅10−5 | 1.79⋅10−5 |
200 × 200 | 5.45⋅10−4 | 7.29⋅10−5 | 5.46⋅10−4 | 7.76⋅10−5 | 1.40⋅10−5 | 4.74⋅10−6 |