most citedPhysics Informed Neural Networks with strong and weak residuals for advection-dominated diffusion problems

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math.NA2024

Stabilization of isogeometric finite element method with optimal test functions computed from norm residual minimization

Marcin Łoś, Tomasz Służalec, Maciej Paszyński +1

We compare several stabilization methods in the context of isogeometric analysis and B-spline basis functions, using an advection-dominated advection\revision{-}diffusion as a mode…

math.NA2023★ 1 cited

Physics Informed Neural Networks with strong and weak residuals for advection-dominated diffusion problems

Maciej Sikora, Patryk Krukowski, Anna Paszynska +1

This paper deals with the following important research questions. Is it possible to solve challenging advection-dominated diffusion problems in one and two dimensions using Physics…