A Posteriori Analysis of a Positive Streamwise Invariant Discretization of a Convection-Diffusion Equation

Authors:
Christine Bernardi;Tomás Chacón Rebollo;Marco Restelli
Affiliations:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Universitéé Pierre et Marie Curie--Paris 6, Paris Cedex 05, France 75252;Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, Sevilla, Spain 41012;Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, Sevilla, Spain 41012
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

We consider the finite element discretization of a convection-diffusion equation, where the convection term is handled via a fluctuation splitting algorithm. We prove a posteriori error estimates which allow us to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.