Table 7 The errors and convergence rates of \(\pmb{u-u^{hk}}\) 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) | 3.2246e − 2 |  | (1/8,1/2) | 1.0582e − 0 |  |
(0.0442,1/8) | 4.1121e − 3 | 2.9712 | (1/27,1/3) | 3.1763e − 1 | 2.9681 |
(0.0156,1/16) | 5.0685e − 4 | 3.0203 | (1/64,1/4) | 1.3257e − 1 | 3.0372 |