The error of the reduced solution for elliptic interface problems is controlled entirely by the approximation error of the interface data, recovering the full solution to roundoff accuracy once the interface is accurate.
LeVeque.Finite Difference Methods for Ordinary and Partial Differential Equations
3 Pith papers cite this work. Polarity classification is still indexing.
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Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.
citing papers explorer
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Interface Reduction for Elliptic Interface Problems with Conservative Flux Reconstruction
The error of the reduced solution for elliptic interface problems is controlled entirely by the approximation error of the interface data, recovering the full solution to roundoff accuracy once the interface is accurate.
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Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.
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