Table 12 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 |
|---|---|---|---|---|---|
(0.125, 1/4) | 9.4944e−2 |  | (1/8, 1/2) | 3.6262e−1 |  |
(0.0442, 1/8) | 1.2179e−3 | 2.9627 | (1/27, 1/3) | 1.0680e−1 | 3.0148 |
(0.0156, 1/16) | 1.5288e−4 | 2.9940 | (1/64, 1/4) | 4.4864e−2 | 3.0149 |