Table 5 The errors and convergence rates of u in \(\pmb{L^{2}(L^{2})}\) and \(\pmb{L^{2}(H^{1})}\) norms about space
From: A space-time continuous finite element method for 2D viscoelastic wave equation
h | \(\boldsymbol{\Vert u-u^{hk}\Vert _{L^{2}(L^{2})}}\) | Rate | \(\boldsymbol{\Vert u-u^{hk}\Vert _{L^{2}(H^{1})}}\) | Rate |
|---|---|---|---|---|
1/8 | 1.0458e−2 |  | 3.5296e−1 |  |
1/16 | 2.5742e−3 | 2.0224 | 1.7909e−1 | 0.9788 |
1/32 | 6.5257e−4 | 1.9799 | 9.0149e−2 | 0.9903 |
1/64 | 1.6514e−4 | 1.9824 | 4.4891e−2 | 1.0059 |