Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions
Overview & Synopsis
Solutions of second-order elliptic PDE problems on nonconvex or cracked domains with mixed Dirichlet-Neumann conditions typically lie outside $H^2(Ω)$. Near re-entrant corners, crack tips and points where the boundary condition changes type, the gradient grows like $r^{λ-1}$ with $λ
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arxiv.org)
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Document Information
| Document Title | Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions |
|---|---|
| Author / Organization | Somnath Giri, Muslim Malik, Rishikesh Yadav |
| Subject & Discipline | math.NA |
| Categories | Science & Mathematics |
| Publication Year | 2026 |
| License / Rights | arXiv Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
arXiv
(arxiv.org)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-273068 |
| Original Source Link | Visit Source Page on arxiv.org » |