Quadratures, Assembling, and Storage

Abstract

This chapter deals with various aspects related to the implementation of the finite element method. It is organized into four sections. The first section is concerned with quadratures, i.e., methods to evaluate integrals approximately. These are almost unavoidable in applications since only a few academic problems involve integrals which can be evaluated analytically. We present various quadratures and evaluate the impact of this type of approximation on the accuracy of the finite element method. In the first section, we also list important arrays (Jacobian, shape functions, derivatives, etc.) which are required in a finite element code. The second section deals with assembling techniques for matrices and right-hand sides. The next section reviews some basic storage techniques for sparse matrices. In the last section, we briefly discuss how to deal with essential boundary conditions, whether homogeneous or not.