. Author manuscript; available in PMC: 2011 Jul 1.

Published in final edited form as: J Comput Phys. 2010 Jul 1;229(13):5208–5227. doi: 10.1016/j.jcp.2010.03.036

Table 3. Convergence property for advection-electrodiffusion.

From the example of Section 6.4, numerical error $E_{p}^{N}$ and convergence ratio $R_{p}^{N}$ are computed on the two-level locally refined grids Ω_N with discrete L_p norms. In addition to the concentrations of two species of Ca²⁺ and Cl⁻, electrical charge density ρ_e, and electrical potential ϕ, fluid velocity u is employed at t = 0.1 ms.

[Ca²⁺] (μM)

[Cl⁻] (μM)

ρ_e (μC)

ϕ (mV)

u (μm/s)

E_{2}^{64}

5.82e-3

1.09e-2

2.778e-4

1.454e-5

4.347e-3

E_{2}^{128}

R_{2}^{64}

3.40e-3

1.71

6.25e-3

1.75

1.561e-4

1.78

8.078e-6

1.80

1.469e-3

2.96

E_{2}^{256}

R_{2}^{128}

1.86e-3

1.83

3.36e-3

1.86

8.528e-5

1.83

4.438e-6

1.82

6.556e-4

2.24

E_{1}^{64}

1.33e-8

2.67e-8

4.756e-10

3.024e-11

1.167e-8

E_{1}^{128}

R_{1}^{64}

7.16e-9

1.86

1.48e-8

1.81

2.571e-10

1.85

1.671e-11

1.81

3.752e-9

3.11

E_{1}^{256}

R_{1}^{128}

3.73e-9

1.92

7.89e-9

1.87

1.375e-10

1.87

8.793e-12

1.90

1.617e-9

2.32