The finite element method (FEM) is a numerical method of solving systems of differential equations. They are used extensively in many fields of engineering because they require very little knowledge of mathematics beyond basic algebra to use. It belongs to the Methods of Weighted residuals in that the problem is formulated such that some conditions are satisfied exactly, while others are satisfied only approximately or numerically (i.e., the "residual" being the difference between the exact solution and the approximate solution is weighted and minimized to get the best approximation).