Galerkin Method

A projection-based approximation method for solving differential and integral equations: one selects a finite-dimensional trial space and enforces that the residual (the PDE or operator applied to the trial solution minus the data) is orthogonal to a chosen test space, yielding a finite system for the expansion coefficients.

A projection-based approach that constructs approximate solutions by requiring the residual of a differential or integral operator to be orthogonal to a chosen test space, yielding a finite system for expansion coefficients.

A projection-based approximation technique for differential or integral equations that seeks approximate solutions in a finite-dimensional subspace by imposing that the residual be orthogonal to that subspace (or a test subspace).