Table 6 The errors and convergence rates of u in the \(\pmb{L^{2}(L^{2})}\) and \(\pmb{L^{2}(H^{1})}\) norms in time
From: A space-time continuous finite element method for 2D viscoelastic wave equation
( h , k ) | \(\boldsymbol{\Vert u-u^{hk}\Vert _{L^{2}(L^{2})}}\) | Rate | ( h , k ) | \(\boldsymbol{\Vert u-u^{hk}\Vert _{L^{2}(H^{1})}}\) | Rate | Â |
|---|---|---|---|---|---|---|
(0.125, 1/4) | 1.0053e−2 |  | (1/8, 1/2) | 3.6314e−1 |  |  |
(0.0442, 1/8) | 1.3166e−3 | 2.9327 | (1/27, 1/3) | 1.0685e−1 | 3.0171 |  |
(0.0156, 1/16) | 1.6673e−4 | 2.9817 | (1/64, 1/4) | 4.4870e−2 | 3.0161 |  |