Abstract
This chapter is devoted to a practical presentation of the finite-element method (FEM). The focus is on the construction of numerical schemes rather than on the numerical properties that this approach benefits; References [5, 106] provide an introduction. A very large literature survey, sorted by fundamental references, mathematical foundations, applications, implementation techniques, and other special topics as well as proceedings of symposia and conferences, can be found in [146].
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Notes
- 1.
A mathematical demonstration is needed to prove that the weak solution, associated to the variational formulation of the problem, is also a solution of the original strong formulation of the Poisson problem.
- 2.
The notion of a derivative must be understood in a weak sense, and the notion of integrability must be considered in the \(L^2\) sense.
- 3.
It is difficult to define the notion of null trace. For our purposes, let us consider its intuitive meaning.
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Mendes, N., Chhay, M., Berger, J., Dutykh, D. (2019). Basics in Practical Finite-Element Method. In: Numerical Methods for Diffusion Phenomena in Building Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-31574-0_4
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DOI: https://doi.org/10.1007/978-3-030-31574-0_4
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