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Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations

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Abstract

We construct and analyze a local discontinuous Galerkin (LDG) method which is combined with the locally one-dimensional method as one of the splitting methods. The proposed method reduces the size of algebraic system of equations due to the splitting technique, as a result computational time is also reduced. We are particularly interested in improving the computational efficiency in comparison to the original schemes, aiming to preserve the properties of the LDG method. We also deal with the method’s stability and convergence analyses and discuss its computational time. Finally, some numerical simulations are carried out to confirm the theoretical results.

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Acknowledgements

The authors would like to express their deep thanks to anonymous referees for their careful reading and invaluable suggestions on this manuscript.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    Somayeh Fouladi & Mohammad Shafi Dahaghin

  2. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Reza Mokhtari

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  1. Somayeh Fouladi
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Correspondence to Somayeh Fouladi.

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Fouladi, S., Mokhtari, R. & Dahaghin, M.S. Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations. Numer Algor 92, 1425–1449 (2023). https://doi.org/10.1007/s11075-022-01347-2

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