3 papers
math.NA2026
ReLU Neural de Rham Complexes
Kaibo Hu, Jindong Wang, Jinchao Xu
We construct finite-dimensional de Rham subcomplexes generated by fixed-neuron shallow ReLU neural networks, a class of spaces known to provide optimal approximation rates. For…
math.NA2024
Interior Penalty Nonconforming Finite Element Methods for -th Order PDEs in
Shuonan Wu, Jinchao Xu
In general -dimensional simplicial meshes, we propose a family of interior penalty nonconforming finite element methods for -th order partial differential equations, where $…
math.NA2024
Integral boundary conditions in phase field models
Xiaofeng Xu, Lian Zhang, Yin Shi +2
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic devic…