When finite elements are used to discretize linear elliptic problems, large linear systems arise whose matrix structures are very particular. They are sparse, which is to say that they possess a very large number of zero entries (see theorems 5.2 and 5.3). It is therefore important to understand the main techniques that are used to solve linear systems, so that the most appropriate one can be chosen depending on the nature of the linear system. This appendix is for those who may have questions about how the finite element method can be implemented in Fortran, C/C++, or any other fast programming language. In the programming environments used within scientific computing (Matlab, Scilab, Octave, Python, Julia, etc.), matrix storage issues and system-solving algorithms are obfuscated by the terminology used (sparse-type in Matlab), but understanding these techniques will be very informative.
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