Error Estimation based on Richardson Expansion
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Error Estimation based on Richardson Expansion
- Consider a 2-level update scheme with Dx = h and Dt = k.
- Let Q be a two-level explicit difference operator and q the order of accuracy in space and time.
- Local truncation error is
- u (x, t+k) - Q u (x, t) = t + k O (kq+1 + hq+1)
- If we take two time steps with method Q, then the local truncation error is
- u (x, t + 2k) - Q2 u (x, t) = 2 t + k O (kq+1 + hq+1)
- Let Q2h denote the same difference method as Q but based on mesh widths of 2h and 2k.
- u (x, t + 2k) - Q2h u (x, t) = 2q+1 t + O (hq+2)
Notes:
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