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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 The convergence rate for \(\pmb{\|c-c_{h}\|}\) in the two-dimensional case

From: Uniform estimate for characteristics-mixed finite element method for two-dimensional advection-dominated transport problems

h  = Δ t

\(\boldsymbol{\|c-c_{h}\|}\)

ε  = 0.001

ε  = 0.0005

ε  = 0.0001

ε  = 0.00005

1/16

0.0025

0.0025

0.0026

0.0026

1/32

0.0017

0.0017

0.0017

0.0017

1/48

8.8193e−04

8.6351e−04

8.6170e−04

8.6252e−04

1/64

6.7982e−04

6.5229e−04

6.4625e−04

6.4692e−04

   

Convergence rate 0.9512

Constant \(\bar{Q}_{1}=0.0205\)

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