Theory and Modern Applications
Table 3 The error for different time step Δt and space step h at \({t=1}\)
(Δt,h) | \(\Vert u-u_{h} \Vert \) | Rate | \(\Vert u-u_{h} \Vert _{1}\) | Rate | \(\Vert u-u_{h} \Vert _{2} \) | Rate |
|---|---|---|---|---|---|---|
(1/1000,1/10) | \(2.6507e^{-4}\) | Â | \(7.1428e^{-3}\) | Â | \(4.3020e^{-1}\) | Â |
(1/8000,1/20) | \(1.2618e^{-5}\) | 4.3928 | \(8.1323e^{-4}\) | 3.1348 | \(1.0389e^{-1}\) | 2.0500 |
(1/64,000,1/40) | \(7.1987e^{-7}\) | 4.1316 | \(9.9738e^{-5}\) | 3.0274 | \(2.5745e^{-2}\) | 2.0127 |
(1/512,000,1/80) | \(4.1744e^{-8}\) | 4.1081 | \(1.2400e^{-5}\) | 3.0078 | \(6.4221e^{-3}\) | 2.0032 |