The finite element method may be viewed as a method for forming a discrete linear system AU = b or nonlinear system b(U) = 0 corresponding to the discretization of the variational form of a differential equation. A central part of the implementation of finite element methods is therefore the computation of matrices and vectors from variational forms. In this chapter, we describe the standard algorithm for computing the discrete operator (tensor) A defined in Chapter [kirby-5]. This algorithm is

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... known as finite element assembly. We also discuss efficiency aspects of the standard algorithm and extensions to matrix-free methods.