# Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

# A Priori and A Posteriori Error Analysis in Chemistry

Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_255

## Synonyms

Convergence analysis; Error estimates; Guaranteed accuracy; Refinement

## Definition

For a numerical discretization chosen to approximate the solution of a given problem or for an algorithm used to solve the discrete problem resulting from the previous discretization, a priori analysis explains how the method behaves and to which extent the numerical solution that is produced from the discretization/algorithm is close to the exact one. It also allows to compare the numerical method of interest with another one. With a priori analysis though, there is no definite certainty that a given computation provides a good enough approximation. It is only when the number of degrees of freedom and the complexity of the computation is large enough that the convergence of the numerical method can be guaranteedly achieved. On the contrary, a posteriori analysis provides bounds on the error on the solution or the output coming out of the simulation. The concept of a posteriori analysis can even...

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