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arXiv · 2402.07749

Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems

Qiang Du·James M. Scott·Xiaochuan Tian
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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.

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Qiang Du, James M. Scott, Xiaochuan Tian. 2024-02-12. Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. https://arxiv.org/abs/2402.07749

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