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Numerical analysis of a least-squares finite element method for the time-dependent advection–diffusion equation

✍ Scribed by R.C. Leal Toledo; V. Ruas

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
340 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

A mixed finite element scheme designed for solving the time-dependent advection-diffusion equations expressed in terms of both the primal unknown and its flux, incorporating or not a reaction term, is studied. Once a time discretization of the Crank-Nicholson type is performed, the resulting system of equations allows for a stable approximation of both fields, by means of classical Lagrange continuous piecewise polynomial functions of arbitrary degree, in any space dimension. Convergence in the norm of H 1 × H(div) in space and in appropriate senses in time applying to this pair of fields is demonstrated.

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