Titlebook: Introduction to Numerical Methods for Variational Problems; Hans Petter Langtangen,Kent-Andre Mardal Textbook 2019 Springer Nature Switzer

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Function Approximation by Global Functions,Many successful numerical solution methods for differential equations, including the finite element method, aim at approximating the unknown function by a sum.

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Function Approximation by Finite Elements,The purpose of this chapter is to use the ideas from the previous chapter on how to approximate functions, but the basis functions are now of finite element type.

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Variational Formulations with Finite Elements,We shall now take the ideas from previous chapters and put together such that we can solve PDEs using the flexible finite element basis functions. This is quite a machinery with many details, but the chapter is mostly an assembly of concepts and details we have already met.

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Time-Dependent Variational Forms,There are at least three different strategies for performing a discretization in time.

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Variational Forms for Systems of PDEs,Many mathematical models involve .?+?1 unknown functions governed by a system of .?+?1 differential equations.