Theory and Modern Applications
Table 2 The error for different time step Δt 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 |
|---|---|---|---|---|---|---|
(1/10,1/800) | \(5.9048e^{-4}\) | Â | \(2.0970e^{-3}\) | Â | \(1.3459e^{-2}\) | Â |
(1/20,1/800) | \(2.7118e^{-4}\) | 1.1226 | \(9.6223e^{-4}\) | 1.1239 | \(6.1815e^{-3}\) | 1.1225 |
(1/40,1/800) | \(1.3035e^{-4}\) | 1.0569 | \(4.6234e^{-4}\) | 1.0574 | \(2.9718e^{-3}\) | 1.0566 |
(1/80,1/800) | \(6.4199e^{-5}\) | 1.0218 | \(2.2765e^{-4}\) | 1.0221 | \(1.4644e^{-3}\) | 1.0210 |