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Involutive Completion to Avoid LBB Condition

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • B. Mohammadi

    (Montpellier University, Mathematics and Modeling Institute)

  • J. Tuomela

    (University of Joensuu, Department of Mathematics)

Abstract

We propose to use the involutive form of a system of PDEs in numerical computations. We illustrate our approach by applying it to the Stokes system. As in the case of the solution of differential algebraic equations our approach takes explicitly into account the integrability conditions of the system which are only implicitly present in the original formulation. The extra calculation cost is negligible while the discrete form becomes much simpler to handle. One interesting consequence is that the discrete formulation needs not to satisfy the classical LBB compatibility condition. The approach is very general and can be useful for a wide variety of systems not as well known as fluid flow equations.

Suggested Citation

  • B. Mohammadi & J. Tuomela, 2008. "Involutive Completion to Avoid LBB Condition," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 497-504, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_59
    DOI: 10.1007/978-3-540-69777-0_59
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