Table 8 The errors and convergence rates of \(\pmb{v-v^{hk}}\) in the \(\pmb{L^{2}(L^{2})}\) and \(\pmb{L^{2}(H^{1})}\) norms concerning k
From: Convergence of a space-time continuous Galerkin method for the wave equation
( h , k ) | Error in \(\boldsymbol{L^{2}(L^{2})}\) | Rate | ( h , k ) | Error in \(\boldsymbol{L^{2}(H^{1})}\) | Rate |
|---|---|---|---|---|---|
(0.125,1/4) | 1.6141e − 2 |  | (1/8,1/2) | 5.2912e − 1 |  |
(0.0442,1/8) | 2.0566e − 3 | 2.9724 | (1/27,1/3) | 1.5882e − 1 | 2.9681 |
(0.0156,1/16) | 2.5788e − 4 | 2.9955 | (1/64,1/4) | 6.6294e − 2 | 3.0369 |