Table 1 Errors norms and the corresponding convergence orders (\(\Delta t\approx \Delta x^{2}\)) for example 2
From: Linear B-spline finite element method for the generalized diffusion equation with delay
N | Central finite difference method (\(\theta =1\)) [30] | Linear B-spline FEM | ||||||
|---|---|---|---|---|---|---|---|---|
\(L_{2}\) | Order | \(L_{\infty }\) | Order | \(L_{2}\) | Order | \(L_{\infty }\) | Order | |
5 | 5.41E−02 | – | 4.10E−02 | – | 2.52E−02 | – | 2.45E−02 | – |
10 | 1.34E−03 | 2.00 | 1.07E−02 | 2.07 | 4.77E−03 | 2.40 | 4.70E−03 | 2.38 |
20 | 3.25E−03 | 2.04 | 2.59E−03 | 2.02 | 1.14E−03 | 2.06 | 1.12E−03 | 2.07 |
40 | 8.10E−04 | 2.00 | 6.46E−04 | 2.00 | 2.83E−04 | 2.01 | 2.76E−04 | 2.02 |
80 | 2.02E−04 | 2.00 | 1.61E−04 | 2.00 | 7.06E−05 | 2.00 | 6.89E−05 | 2.00 |