Table 2 Numerically found values of \(\tau\) that minimize \(| kh - k^h(\theta ) h|\) for all \(\theta\) in the \(p=0\) case
From: Stabilization in relation to wavenumber in HDG methods
kh | Optimal \(\tau\), | Optimal \(\tau\), |
|---|---|---|
\({\mathrm {Im}}(\tau )>0\) | \({\mathrm {Im}}(\tau )<0\) | |
\(\pi /4\) | \(0.807\hat{\imath }\) | \(-0.931\hat{\imath }\) |
\(\pi /8\) | \(0.837\hat{\imath }\) | \(-0.898\hat{\imath }\) |
\(\pi /16\) | \(0.851\hat{\imath }\) | \(-0.882\hat{\imath }\) |
\(\pi /32\) | \(0.859\hat{\imath }\) | \(-0.874\hat{\imath }\) |
\(\pi /64\) | \(0.863\hat{\imath }\) | \(-0.871\hat{\imath }\) |
\(\pi /128\) | \(0.865\hat{\imath }\) | \(-0.868\hat{\imath }\) |
\(\pi /256\) | \(0.866\hat{\imath }\) | \(-0.867\hat{\imath }\) |