Table 6 The errors and convergence rates of \(\pmb{v-v^{hk}}\) in the \(\pmb{L^{2}}\) and \(\pmb{H^{1}}\) norms concerning k at \(\pmb{t=1}\)
From: Convergence of a space-time continuous Galerkin method for the wave equation
( h , k ) | Error in \(\boldsymbol{L^{2}}\) | Rate | ( h , k ) | Error in \(\boldsymbol{H^{1}}\) | Rate |
|---|---|---|---|---|---|
(0.125,1/4) | 1.2556e − 2 |  | (1/8,1/2) | 4.0417e − 1 |  |
(0.0442,1/8) | 1.5500e − 3 | 3.0181 | (1/27,1/3) | 1.2116e − 1 | 2.9712 |
(0.0156,1/16) | 1.1918e − 4 | 3.7010 | (1/64,1/4) | 5.0577e − 2 | 3.0367 |