3 papers
math.NA2026
RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
Pablo Herrera, Jamie M. Taylor, Carlos Uriarte +3
Solving Partial Differential Equations (PDEs) using neural networks presents different challenges, including integration errors and spectral bias, often leading to poor approximati…
math.NA2023
A DPG method for the quad-curl problem
Thomas Führer, Pablo Herrera, Norbert Heuer
We derive an ultraweak variational formulation of the quad-curl problem in two and three dimensions. We present a discontinuous Petrov-Galerkin (DPG) method for its approximation a…
math.NA2021
DPG methods for a fourth-order div problem
Thomas Führer, Pablo Herrera, Norbert Heuer
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and secon…