Solving an Advection–Diffusion Equation by a Finite Element Method

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 5 in An Introduction to Scientific Computing, 2023, pp 105-128 from Springer

Abstract: Abstract Stiff differential equations appear in a wide range of mathematical models used in biology, chemistry, mechanics, etc. These are equations with solutions containing several time scales. Parts of the solution vary slowly, while other parts vary rapidly. Classical numerical schemes require a small time step to compute accurately the solution since it is necessary to capture rapid time scales. In this chapter, we consider a 1D advection-diffusion equation with a solution varying abruptly near one endpoint, making difficult to compute the solution in a reasonable time. We show how a finite-element stabilization method overcomes this difficulty.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_5

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