Published in:
Numerical Methods for Partial Differential Equations, 40 (2024) 6
Language:
English
DOI:
10.1002/num.23145
ISSN:
0749-159X;
1098-2426
Origination:
Footnote:
Description:
AbstractIn this work, an efficient and stable exponential time difference method is presented for solving boundary layer problems. By combining exponential time difference schemes with spatial direct discontinuous Galerkin discretization based on exponential boundary layer approximations, the proposed algorithm not only may admit large time step sizes but also could provide good spatial approximations even if on rather coarse spatial grids in the boundary layer. Some energy stabilities of the numerical scheme are rigorously derived. Numerical examples illustrate the accuracy, stability and efficiency of the algorithm.