4 papers
Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries
Charalambos Makridakis, Aaron Pim, Tristan Pryer +1
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network a…
A posteriori certification of PDE approximations with particular application to neural networks
Lewin Ernst, Nikolaos Rekatsinas, Karsten Urban
We propose rigorous and efficiently computable lower and upper a posteriori error bounds for given approximations to PDEs on a given domain, which might be geometrically complex. T…
A quadratic finite element wavelet Riesz basis
Nikolaos Rekatsinas, Rob Stevenson
In this paper, continuous piecewise quadratic finite element wavelets are constructed on general polygons in . The wavelets are stable in for …
An optimal adaptive wavelet method for First Order System Least Squares
Nikolaos Rekatsinas, Rob Stevenson
In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet…