A Refined Nonlocal Approach to Elliptic Transmission Problems on Manifolds

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This research aims to develop a refined nonlocal model for accurately approximating elliptic transmission problems on manifolds.
Developed nonlocal modeling method utilizing integral approximation of the Laplace-Beltrami operator (LBO) at smooth interfaces.
Reconstructed transmission conditions through a nonlocal averaging mechanism.
Established the well-posedness of the nonlocal model and its second-order convergence to corresponding local solutions.
Demonstrated second-order truncation accuracy without introducing second-order normal derivatives.
Theoretical proof confirmed convergence rates towards the corresponding local solution.
Numerical examples validated the theoretical convergence rate via point cloud integration method.

Demonstrates improved modeling of elliptic transmission problems, indicating enhanced accuracy on manifolds.

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Qiao et al. (2026) studied this question.

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