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math.NA2025
An Adaptive Algorithm Based on Stochastic Discontinuous Galerkin for Convection Dominated Equations with Random Data
Pelin ÃiloÄlu, Hamdullah Yücel
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated eq…
math.NA2025
Energy Dissipation Preserving Physics Informed Neural Network for Allen-Cahn Equations
Mustafa Kütük, Hamdullah Yücel
This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic an…