# Galerkin approximation

From Glossary of Meteorology

## Galerkin approximation

An approximation to a differential equation that uses a linear combination of basis functions with weights determined by minimizing a globally integrated measure of the error in the solution.

The resulting error is orthogonal to each basis function in an integral sense. Finite-element approximations result when piecewise linear basis functions are selected. Spectral approximations are produced when spherical harmonic basis functions are selected over spherical domains.

*See*finite-element model.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.