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.

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