True error (based on an exact solution) is not usually available – if we had this, why would we even use numerical methods? Thus, you generally want to use approximate (estimated) error instead like:
No systematic, general approach for error estimation for all problems, as specific methods use different approaches.This can be used when the true value is unknown. This is also used in iterative methods, where in each subsequent trial, the approximate value gets closer to the true value.
Link to original
Some guidelines:
- Avoid subtracting two nearly equal numbers
- Do not add very small and very large numbers together
Error control methods:
- Sensitivity analysis, such as grid refinement study or sensitivity to variations in input parameters
- Examine limiting cases (e.g. upper/lower bounds)