Abstract
In this presentation we will discuss a domain decomposition technique for advection equations of the following type:
where f is given and b(u) is a transport field possibly depending upon the unknown u. This equation has to be fulfilled in a spatial region and suitable conditions at the boundary of this region and at the initial time must be prescribed. As a matter of fact, our analysis will be carried out on a linearized, time independent version of equation (1.1) (to this case one can always reduce after a time discretization and a suitable linearization of the nonlinear term b(u)). More precisely, we shall consider the following boundary value problem
where Ω is a two dimensional domain, b, f and b 0 are assigned functions in Ω and g is a given function defined in the portion ∂Ω in of the boundary of Ω along which the transport enters Ω (∂Ωn in is said to be the “inflow boundary”).
The following institutions have provided a partial support for this work: Istituto di Analisi Numerica del Consiglio Nazionale delle Ricerche (Pavia, Italy), Ministero dell’Università e della Ricerca Scientifica e Tecnologica (Italy), Institute for Mathematics and its Applications (funds provided by the National Science Foundation).
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References
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© 1993 Springer-Verlag New York, Inc.
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Gastaldi, F. (1993). A Multidomain Decomposition for the Transport Equation. In: Friedman, A., Spruck, J. (eds) Variational and Free Boundary Problems. The IMA Volumes in Mathematics and its Applications, vol 53. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8357-4_7
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DOI: https://doi.org/10.1007/978-1-4613-8357-4_7
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