TY - JOUR
T1 - Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions
AU - Kim, Philsu
AU - Kim, Dojin
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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.
AB - 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.
KW - Burgers’ equation
KW - Convergence analysis
KW - Non-linear advection–diffusion equation
KW - Semi-Lagrangian method
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=85072585525&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2019.124744
DO - 10.1016/j.amc.2019.124744
M3 - Article
AN - SCOPUS:85072585525
SN - 0096-3003
VL - 366
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 124744
ER -