Finite element method

Summary

The finite element method is a way to compute approximate solutions of boundary value problems for partial differential equations. It writes the problem in weak form and splits the domain into small pieces such as triangles. Then it looks for the best approximation among functions that are polynomials on each piece. It is a Galerkin method whose basis functions are supported on a few pieces, so it leads to a large sparse linear system. It handles complicated geometries well and is the standard tool of engineering simulation in structural mechanics, heat flow and electromagnetism.