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ANALYSIS OF AN INTERFACE STABILIZED FINITE ELEMENT METHOD: THE ADVECTION-DIFFUSION-REACTION EQUATION


Type

Article

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Authors

Wells, GN 

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 L2 norm. The analysis results are supported by a number of numerical experiments.

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Keywords

finite element methods, discontinuous Galerkin methods, advection-diffusion-reaction, DISCONTINUOUS GALERKIN METHODS, HYPERBOLIC PROBLEMS

Journal Title

SIAM J NUMER ANAL

Conference Name

Journal ISSN

0036-1429
1095-7170

Volume Title

Publisher

Society for Industrial & Applied Mathematics (SIAM)