Convergence in the maximum norm of ADI-type methods for parabolic problems
Numerical Analysis
2021-02-25 v1 Numerical Analysis
Abstract
Results on unconditional convergence in the Maximum norm for ADI-type methods, such as the Douglas method, applied to the time integration of semilinear parabolic problems are quite difficult to get, mainly when the number of space dimensions is greater than two. Such a result is obtained here under quite general conditions on the PDE problem in case that time-independent Dirichlet boundary conditions are imposed. To get these bounds, a theorem that guarantees, in some sense, power-boundeness of the stability function independently of both the space and time resolutions is proved.
Cite
@article{arxiv.2102.12229,
title = {Convergence in the maximum norm of ADI-type methods for parabolic problems},
author = {S. Gonzalez Pinto and D. Hernandez Abreu},
journal= {arXiv preprint arXiv:2102.12229},
year = {2021}
}