Convergence of fully discrete implicit and semi-implicit approximations of nonlinear parabolic equations
Abstract
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the -Laplace operator since the latter lead to linear systems of equations in the time steps. The semi-implicit treatment of the operator requires introducing a regularization parameter that has to be suitably related to other discretization parameters. To avoid restrictive, unpractical conditions, a careful convergence analysis has to be carried out. The arguments presented in this article show that convergence holds under a moderate condition that relates the step size to the regularization parameter but which is independent of the spatial resolution.
Keywords
Cite
@article{arxiv.1902.08122,
title = {Convergence of fully discrete implicit and semi-implicit approximations of nonlinear parabolic equations},
author = {Sören Bartels and Michael Růžička},
journal= {arXiv preprint arXiv:1902.08122},
year = {2019}
}