Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
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| Format: | Preprint |
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2024
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| _version_ | 1866929241151504384 |
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| author | Du, Qiang Scott, James M. Tian, Xiaochuan |
| author_facet | Du, Qiang Scott, James M. Tian, Xiaochuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems Du, Qiang Scott, James M. Tian, Xiaochuan Numerical Analysis 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. |
| title | Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.07749 |