Table 7 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 | \(\boldsymbol{\nonumber \Vert u_{N}-u_{N}^{hk}\Vert _{H^{1}}}\) | Rate |
|---|---|---|---|---|
1/8 | 2.9254e−3 |  | 2.0047e−1 |  |
1/16 | 6.8669e−4 | 2.0909 | 1.0049e−1 | 0.9963 |
1/32 | 1.8210e−4 | 1.9149 | 5.0419e−2 | 0.9950 |
1/64 | 4.5634e−5 | 1.9965 | 2.5113e−2 | 1.0055 |