Error estimates for a class of discontinuous Galerkin methods for nonsmooth problems via convex duality relations
Numerical Analysis
2020-04-21 v1 Numerical Analysis
Abstract
We devise and analyze a class of interior penalty discontinuous Galerkin methods for nonlinear and nonsmooth variational problems. Discrete duality relations are derived that lead to optimal error estimates in the case of total-variation regularized minimization or obstacle problems. The analysis provides explicit estimates that precisely determine the role of stabilization parameters. Numerical experiments suppport the optimality of the estimates.
Cite
@article{arxiv.2004.09196,
title = {Error estimates for a class of discontinuous Galerkin methods for nonsmooth problems via convex duality relations},
author = {Sören Bartels},
journal= {arXiv preprint arXiv:2004.09196},
year = {2020}
}