Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
Numerical Analysis
2024-02-13 v1 Numerical Analysis
Abstract
We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on variational convergence, or Gamma-convergence. We demonstrate the broad applicability of the theoretical framework by developing asymptotically compatible finite element discretizations of some representative nonlinear nonlocal variational problems on a bounded domain. These include nonlocal nonlinear problems with classically-defined, local boundary constraints through heterogeneous localization at the boundary, as well as nonlocal problems posed on parameter-dependent domains.
Keywords
Cite
@article{arxiv.2402.07749,
title = {Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems},
author = {Qiang Du and James M. Scott and Xiaochuan Tian},
journal= {arXiv preprint arXiv:2402.07749},
year = {2024}
}