Table 1 The errors and convergence rates of u 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 | \(\boldsymbol{\Vert u_{N}-u_{N}^{hk}\Vert _{L^{2}}}\) | Rate | \(\boldsymbol{\Vert u_{N}-u_{N}^{hk}\Vert _{H^{1}}}\) | Rate |
|---|---|---|---|---|
1/8 | 1.4439e−2 |  | 4.8570e−1 |  |
1/16 | 3.5585e−3 | 2.0207 | 2.4646e−1 | 0.9787 |
1/32 | 9.0532e−4 | 1.9748 | 1.2406e−1 | 0.9903 |
1/64 | 2.3248e−4 | 1.9613 | 6.1777e−2 | 1.0059 |