Theory and Modern Applications
Table 2 Convergence order of the LDG method with \(\vec{\mathtt {C}}_{12}=(1/\sqrt{2}, 1/\sqrt{2})\) and speed \(c=1/2\)
From: Error estimates of a semi-discrete LDG method for the system of damped acoustic wave equation
\(\mathtt{C}_{11}=\mathtt{C}_{22}\) | \(\sigma_{p}=\sigma_{\vec{q}}=\sigma\) | ||
|---|---|---|---|
|  | σ = 2.0 | σ = 1 | σ = 1/2 |
| Â | \(e_{h}\) | \(e_{h}\) | \(e_{h}\) |
\(\mathtt{C}_{11}=\mathtt{C}_{22}=1/5\) | 1.460 | 1.418 | 1.398 |
\(\mathtt{C}_{11}=\mathtt{C}_{22}=1/10\) | 1.480 | 1.514 | 1.493 |
\(\mathtt{C}_{11}=\mathtt{C}_{22}=1/20\) | 1.475 | 1.441 | 1.424 |