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<p>This paper investigates the dynamics of a nonlocal quasilinear parabolic problem under spatial discretization. Specifically, when the underlying domain is an open polygon, we demonstrate the upper semicontinuity of global attractors associated with the finite element approximation systems. Moreover, if all equilibrium points of the original problem are hyperbolic, the global attractors are lower semicontinuous with respect to the mesh parameter. Based on these results and the continuity of attractors under domain perturbations, we construct a family of attractors in finite-dimensional spaces that converges to the global attractor of the underlying problem posed in an open bounded domain with Lipschitz boundary.</p>

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Finite Element Approximations of the Global Attractor for a Nonlocal Quasilinear Problem

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Xiaoqing Yang,
  • Alexandre N. Carvalho,
  • Chunyou Sun

摘要

This paper investigates the dynamics of a nonlocal quasilinear parabolic problem under spatial discretization. Specifically, when the underlying domain is an open polygon, we demonstrate the upper semicontinuity of global attractors associated with the finite element approximation systems. Moreover, if all equilibrium points of the original problem are hyperbolic, the global attractors are lower semicontinuous with respect to the mesh parameter. Based on these results and the continuity of attractors under domain perturbations, we construct a family of attractors in finite-dimensional spaces that converges to the global attractor of the underlying problem posed in an open bounded domain with Lipschitz boundary.