Skip to main content

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 \(\tau\),
  \({\mathrm {Im}}(\tau )>0\) \({\mathrm {Im}}(\tau )<0\)
\(\pi /4\) \(0.807\hat{\imath }\) \(-0.931\hat{\imath }\)
\(\pi /8\) \(0.837\hat{\imath }\) \(-0.898\hat{\imath }\)
\(\pi /16\) \(0.851\hat{\imath }\) \(-0.882\hat{\imath }\)
\(\pi /32\) \(0.859\hat{\imath }\) \(-0.874\hat{\imath }\)
\(\pi /64\) \(0.863\hat{\imath }\) \(-0.871\hat{\imath }\)
\(\pi /128\) \(0.865\hat{\imath }\) \(-0.868\hat{\imath }\)
\(\pi /256\) \(0.866\hat{\imath }\) \(-0.867\hat{\imath }\)