In numerical analysis, computational physics, and simulation, discretization error is a error resulting from a fact that a function of a continuous variable is represented in the data processor by a finite number of evaluations, for example, on a lattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost.
In signal processing, the analog of discretization is sampling, & results in no loss if the conditions of the sampling theorem are satisfied, otherwise the resulting error is called aliasing.
Discretization error, which arises from finite resolution in the domain, should not be confused with quantization error, which is finite resolution in the range values, nor in round-off error arising from floating-point arithmetic. Discretization error would arise even whether it were possible to represent the values precisely and use exact arithmetic – it is for the error from representing a function by its values at a discrete mark of points, non an error in these values.