39 citations · 43 across the 7 of their papers we have counts for
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PINN-DG: Residual neural network methods trained with Finite Elements
Georgios Grekas, Charalambos G. Makridakis, Tristan Pryer
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integ…
Convergence of Discontinuous Galerkin Methods for Quasiconvex and Relaxed Variational Problems
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular,…
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…
A class of Discontinuous Galerkin methods for nonlinear variational problems
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming f…
Approximations of energy minimization in cell-induced phase transitions of fibrous biomaterials: -convergence analysis
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
We consider a model of energy minimization arising in the study of the mechanical behavior caused by cell contraction within a fibrous biological medium. The macroscopic model is b…