Table 2 The errors and convergence rates of \(\pmb{v-v^{hk}}\) in the \(\pmb{L^{2}}\) and \(\pmb{H^{1}}\) norms concerning h at \(\pmb{t=1}\)
From: Convergence of a space-time continuous Galerkin method for the wave equation
h | Error in \(\boldsymbol{L^{2}}\) | Rate | Error in \(\boldsymbol{H^{1}}\) | Rate |
|---|---|---|---|---|
1/8 | 2.4889e − 2 |  | 8.0276e − 1 |  |
1/16 | 6.2303e − 3 | 1.9981 | 4.0410e − 1 | 0.9903 |
1/32 | 1.4268e − 3 | 2.1266 | 2.0268e − 1 | 0.9955 |
1/64 | 2.3105e − 4 | 2.6265 | 1.0109e − 1 | 1.0036 |