Table 8 The errors and convergence rates of u at \(\pmb{t=t_{N}}\) in the \(\pmb{L^{2}}\) and \(\pmb{H^{1}}\) norms in time
From: A space-time continuous finite element method for 2D viscoelastic wave equation
( h , k ) | \(\boldsymbol{\Vert u_{N}-u_{N}^{hk}\Vert _{L^{2}}}\) | Rate | ( h , k ) | \(\boldsymbol{\Vert u_{N}-u_{N}^{hk}\Vert _{H^{1}}}\) | Rate |
|---|---|---|---|---|---|
(0.125, 0.25) | 4.6260e−3 |  | (1/8, 1/2) | 2.0234e−1 |  |
(0.0442, 0.125) | 4.3551e−4 | 3.4090 | (1/27, 1/3) | 6.0357e−2 | 2.9834 |
(0.0156, 0.0625) | 5.0465e−5 | 3.1093 | (1/64, 1/4) | 2.5314e−2 | 3.0204 |