When using schemes like euler explicit or implicit, Runge-Kutta, Newton etc. one uses these methods to approximate the solution and we get an error over time. How does our "solver" know what the exact solution is when we do not explicitly give an exact solution?
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But for the error there has to be a reference like an exact solution otherwise you could not define a local or global error. I thought about residuals in this sense but this does still does not answer my question..unfortunately. Does my explanation/question somehow make sense? – MatlabNewb Nov 26 '18 at 21:25
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Thanks for your patience and comment :) My problem is that I imagine some let's say fluid solver and it has the Navier Stokes equation implemented. Does the solver simply compare the solution from one time step to the next one hoping that the error will decrease? And that decrease is then represented in the residual (however this was normalized). Can I imagine it like that? If you have any other resources for that topic I would be more than happy. – MatlabNewb Nov 26 '18 at 21:42