149 citations · 414 across the 23 of their papers we have counts for
4 papers · 1 filter
Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
Omar Lakkis, Charalambos Makridakis
We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite el…
A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics…
Deep Uzawa for PDE constrained optimisation
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
In this work, we present a numerical solver for optimal control problems constrained by linear and semi-linear second-order elliptic PDEs. The approach is based on recasting the pr…
Deep Ritz-Finite Element methods: Neural Network Methods trained with Finite Elements
Georgios Grekas, Charalambos G. Makridakis
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $Ω\su…