Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions

2026-10-20来源 arXiv cs.NAEnglish
arXiv:2610.26458v1 Announce Type: new Abstract: Solutions of second-order elliptic PDE problems on nonconvex or cracked domains with mixed Dirichlet-Neumann conditions typically lie outside $H^2(\Omega)$. Near re-entrant corners, crack tips and points where the boundary condition changes type, the gradient grows like $r^{\lambda-1}$ with $\lambda

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