Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions

Philsu Kim and Dojin Kim

Applied Mathematics and Computation, 2020, vol. 366, issue C

Abstract: In this paper, we present a concrete analysis of the convergence and stability of a backward semi-Lagrangian method for a non-linear advection-diffusion equation with the Dirichlet boundary conditions. The total time derivative and the diffusion term are discretized by BDF2 and the second-order central finite difference, respectively, together with the local Lagrangian interpolation. The Cauchy problem for characteristic curves is resolved by an error correction method based on a quadratic polygon. Under the mesh restriction ▵t=O(▵x1/2) between the temporal step size △t and the spatial grid size △x, it turns out that the proposed method has the convergence order O(▵t2+▵x2+▵xp+1/▵t) in the sense of the discrete H1-norm, where p is the degree of an interpolation polynomial. Further, the unconditional stability of the method is established. Numerical tests are presented to support the theoretical analyses.

Keywords: Burgers’ equation; Semi-Lagrangian method; Non-linear advection–diffusion equation; Convergence analysis; Stability analysis (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307362

DOI: 10.1016/j.amc.2019.124744

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