Theory and Modern Applications
Table 1 Table of errors in the \(L^{2}(\varOmega )\) and energy norms
From: A new mixed discontinuous Galerkin method for the electrostatic field
h | \(\| u - u^{h}\|_{L^{1}(\varOmega )}\) | \(\| u - u^{h}\|_{0,\varOmega }\) | \(\| u - u^{h}\|_{h}\) | \(\| p - p^{h}\|_{L^{1}(\varOmega )}\) | \(\| p - p^{h}\|_{L^{2}(\varOmega )}\) | \(\| p - p^{h}\|_{h}\) |
|---|---|---|---|---|---|---|
0.4367 | 0.3471E−01 | 0.2109E−01 | 0.1305E+00 | 0.7633E−01 | 0.1045E+00 | 0.8891E+00 |
0.2184 | 0.6913E−02 | 0.2540E−02 | 0.3875E−01 | 0.1325E−01 | 0.1700E−01 | 0.2229E+00 |
0.1733 | 0.3846E−02 | 0.8845E−03 | 0.2051E−01 | 0.8522E−02 | 0.1134E−01 | 0.1700E+00 |
9.268E−02 | 0.1434E−02 | 0.9734E−04 | 0.4521E−02 | 0.5440E−02 | 0.7059E−02 | 0.6283E−01 |
7.703E−02 | 0.6172E−03 | 0.5080E−04 | 0.3111E−02 | 0.5277E−02 | 0.6941E−02 | 0.4660E−01 |