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

Authors:
R. C. Leal Toledo;V. Ruas
Affiliations:
Departamento de Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro state, Brazil and Programa de Pós-Graduação em Ciência da Co ...;Programa de Pós-Graduação em Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro state, Brazil and UPMC University Paris 6, UMR 7190, ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 3
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Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

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Abstract

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^1xH(div) in space and in appropriate senses in time applying to this pair of fields is demonstrated.