Table 9 The errors and convergence rates of v at \(\pmb{t=t_{N}}\) in the \(\pmb{L^{2}}\) and \(\pmb{H^{1}}\) norms in space
From: A space-time continuous finite element method for 2D viscoelastic wave equation
h | \(\boldsymbol{\Vert v_{N}-v_{N}^{hk}\Vert _{L^{2}}}\) | Rate | \(\boldsymbol{\Vert v_{N}-v_{N}^{hk}\Vert _{H^{1}}}\) | Rate |
|---|---|---|---|---|
1/8 | 1.3422e−2 |  | 2.1612e−1 |  |
1/16 | 3.3845e−3 | 1.9876 | 1.0199e−1 | 1.0833 |
1/32 | 8.5281e−4 | 1.9887 | 5.0673e−2 | 1.0092 |
1/64 | 2.2460e−4 | 1.9249 | 2.5147e−2 | 1.0108 |