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Testing a manufactured solution
- Introduce common mesh parameter: h=\Delta t , \Delta x =ch/C
- This h keeps C and \Delta t/\Delta x constant
- Select coarse mesh h : h_0
- Run experiments with h_i=2^{-i}h_0 (halving the cell size), i=0,\ldots,m
- Record the error E_i and h_i in each experiment
- Compute pariwise convergence rates r_i=
\ln E_{i+1}/E_{i}/\ln h_{i+1}/h_{i}
- Verification: r_i\rightarrow 2 as i increases
