Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
<|reference_start|>Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems: 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.<|reference_end|>
@article{du2024asymptotically,
    title={Asymptotically compatible schemes for nonlinear variational models via
  Gamma-convergence and applications to nonlocal problems},
    author={Qiang Du, James M. Scott, Xiaochuan Tian},
    journal={arXiv preprint arXiv:2402.07749},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.07749},
    primaryClass={math.NA cs.NA}
}