 ##  [Galerkin Method](/galerkin-method) 

  ##  [Galerkin Method](https://natural.quantumdictionary.io/galerkin-method-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

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.

 
 ##  [Galerkin Method](https://mathlogic.quantumdictionary.io/galerkin-method-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

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.

 
 ##  [Galerkin Method](https://puremath.quantumdictionary.io/galerkin-method-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

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).