Table 2 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) | 7.1268e−3 |  | (1/8, 1/2) | 2.0646e−1 |  |
(0.0442, 0.125) | 8.3093e−4 | 3.1005 | (1/27, 1/3) | 6.0569e−2 | 3.0244 |
(0.0156, 0.0625) | 1.0239e−4 | 3.0206 | (1/64, 1/4) | 2.5331e−2 | 3.0302 |