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Solving an Advection–Diffusion Equation by a Finite Element Method

In: An Introduction to Scientific Computing

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Solving an Advection–Diffusion Equation by a Finite Element Method," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 105-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_5
    DOI: 10.1007/978-3-031-35032-0_5
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