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math.NA2025
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…
math.NA2025
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,…