Finite Element Method

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.

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.