##  [Finite Element Method](/finite-element-method) 

  ##  [Finite Element Method](https://natural.quantumdictionary.io/finite-element-method-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A numerical technique for approximating solutions of partial differential equations and variational problems by subdividing the domain into small, simple-shaped elements and using piecewise polynomial basis functions to build a global approximate solution.

 

 

 

 

 





 

 



 ##  [Finite Element Method](https://puremath.quantumdictionary.io/finite-element-method-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A numerical variational technique that approximates solutions of boundary-value problems by replacing infinite-dimensional trial spaces with piecewise polynomial finite-dimensional spaces defined on a mesh, leading to sparse algebraic systems solvable by linear or nonlinear solvers.