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

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...

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Bibliographic Details
Published in:Numerical algorithms 2023-02, Vol.92 (2), p.1425-1449
Main Authors: Fouladi, Somayeh, Mokhtari, Reza, Dahaghin, Mohammad Shafi
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computational efficiency
Computer Science
Computing time
Convection-diffusion equation
Decomposition
Galerkin method
Mathematical analysis
Methods
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Splitting
Stability analysis
Theory of Computation
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01347-2