Geodesic
Alternating direction explicit methods for convection diffusion equations
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 2, pp. 309-325 
Zuzana Buckova; Matthias Ehrhardt; Michael Günther; Zuzana Buckova; Matthias Ehrhardt; Michael Günther. Alternating direction explicit methods for convection diffusion equations. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 2, pp. 309-325. http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a10/
@article{AMUC_2015_84_2_a10,
     author = {Zuzana Buckova and Matthias Ehrhardt and Michael G\"unther and Zuzana Buckova and Matthias Ehrhardt and Michael G\"unther},
     title = { Alternating direction explicit methods for convection diffusion equations},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {309--325},
     year = {2015},
     volume = {84},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a10/}
}
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AU  - Matthias Ehrhardt
AU  - Michael Günther
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AU  - Matthias Ehrhardt
AU  - Michael Günther
TI  - Alternating direction explicit methods for convection diffusion equations
JO  - Acta mathematica Universitatis Comenianae
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%A Matthias Ehrhardt
%A Michael Günther
%T Alternating direction explicit methods for convection diffusion equations
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 309-325
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%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a10/
%F AMUC_2015_84_2_a10

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In this work we investigate the stability and consistency properties of alternating direction explicit (ADE) finite difference schemes applied to convection-diffusion-reaction equations. Employing different discretization strategies of the convection term we obtain various ADE schemes and study their stability and consistency properties. An ADE scheme consists of two sub steps (called upward and downward sweeps) where already computed values at the new time level are used in the discretization stencil. For linear convection-diffusion-reaction equations the consistency of the single sweeps is of order O(k^2 + h^2 + k/h) , but the average of these two sweeps has a consistency of order O(k^2 + h^2), where k, h denote the step size in time and space.