Paper Info
Title
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
Abstract
Analysis of an interface stabilized 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.
Year
DOI
Venue
2011
10.1137/090775464
SIAM J. Numerical Analysis
Keywords
Field
DocType
finite element method,good stability property,advection-diffusion-reaction equation,advection-dominated problem,advection-diusio,continuous galerkin method,discontinuous galerkin method,advection-dominated case,standard convergence rate,interface stabilized finite element,discontinuous galerkin methods,finite element methods,order convergence,stability property,lowest order element,degree of freedom,numerical analysis,galerkin method,convergence rate
Convergence (routing),Discontinuous Galerkin method,Mathematical optimization,Mathematical analysis,Galerkin method,Scalar (physics),Extended finite element method,Finite element method,Mathematics,hp-FEM,Mixed finite element method
Journal
Volume
Issue
ISSN
49
1
SIAM J. Numer. Anal. 49(1), 2011, 87-109
Citations 
PageRank 
References 
8
0.80
11
Authors
1
Name
Order
Citations
PageRank
Garth N. Wells120220.08