Proves a single a priori H1 error bound for consistent CutPINNs using discrete L^gamma interior loss (gamma = 1 + 1/log m_til) and discrete H^{1/2} boundary trace norm on curved level-set domains, with rate limited by cut-cell floor 1/(2 gamma).
Title resolution pending
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
fields
math.NA 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Introduces Consistent CutPINN with discrete H^{1/2} surrogate on C^2 curves, proves chord-arc equivalence and H^1 error bounds, and shows improved accuracy on disk and flower domains for 2D elliptic problems.
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
citing papers explorer
-
Consistent CutPINNs for Convection-Diffusion Equations on Curved Level-Set Domains
Proves a single a priori H1 error bound for consistent CutPINNs using discrete L^gamma interior loss (gamma = 1 + 1/log m_til) and discrete H^{1/2} boundary trace norm on curved level-set domains, with rate limited by cut-cell floor 1/(2 gamma).
-
Consistent CutPINNs for Elliptic PDEs on Curved Level-Set Domains
Introduces Consistent CutPINN with discrete H^{1/2} surrogate on C^2 curves, proves chord-arc equivalence and H^1 error bounds, and shows improved accuracy on disk and flower domains for 2D elliptic problems.
-
Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.