Analysis of an interface stabilised finite element method: The advection-diffusion-reaction equation
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Publication Date
2009-10-29ISSN
0036-1429
Language
English
Type
Article
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Wells, G. (2009). Analysis of an interface stabilised finite element method: The advection-diffusion-reaction equation. http://www.dspace.cam.ac.uk/handle/1810/221724
Abstract
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same number of global degrees of freedom as a continuous Galerkin method on a given mesh and the stability properties of discontinuous Galerkin methods for advection dominated problems. Simulations using the approach in other works demonstrated good stability properties with minimal numerical dissipation, and standard convergence rates for the lowest order elements were observed. In this work, stability of the formulation, in the form of an inf-sup condition for the hyperbolic limit and coercivity for the elliptic case,
is proved, as is order $k+1/2$ order convergence for the advection-dominated case
and order $k +1$ convergence for the diffusive limit in the $L^{2}$ norm. The analysis results are supported by a number of numerical experiments.
Keywords
Finite element methods, discontinuous Galerkin methods, advection-diffusion-reaction
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This record's URL: http://www.dspace.cam.ac.uk/handle/1810/221724
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