Table 10 The errors and convergence rates of v 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 ) | \(\boldsymbol{\Vert v_{N}-v_{N}^{hk}\Vert _{L^{2}}}\) | Rate | ( h , k ) | \(\boldsymbol{\Vert v_{N}-v_{N}^{hk}\Vert _{H^{1}}}\) | Rate |
|---|---|---|---|---|---|
(0.125, 1/4) | 1.3732e−2 |  | (1/8, 1/2) | 2.2904e−1 |  |
(0.0442, 1/8) | 1.7806e−3 | 2.9471 | (1/27, 1/3) | 6.1171e−2 | 3.2561 |
(0.0156, 1/16) | 2.2889e−4 | 2.9596 | (1/64, 1/4) | 2.5366e−2 | 3.0598 |