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

Philsu Kim, Dojin Kim

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish
Article number124744
JournalApplied Mathematics and Computation
Volume366
DOIs
StatePublished - 1 Feb 2020

Keywords

  • Burgers’ equation
  • Convergence analysis
  • Non-linear advection–diffusion equation
  • Semi-Lagrangian method
  • Stability analysis

Fingerprint

Dive into the research topics of 'Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions'. Together they form a unique fingerprint.

Cite this