Table 11 The errors and convergence rates of u in the \(\pmb{L^{2}(L^{2})}\) and \(\pmb{L^{2}(H^{1})}\) norms in 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 | 9.5581e−3 |  | 3.5267e−1 |  |
1/16 | 2.3449e−3 | 2.0272 | 1.7901e−1 | 0.9782 |
1/32 | 5.9563e−4 | 1.9771 | 9.0108e−2 | 0.9903 |
1/64 | 1.5021e−4 | 1.9874 | 4.4884e−2 | 1.0054 |