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math.NA2024
Two and three dimensional -conforming finite element approximations without -elements
Mark Ainsworth, Charles Parker
We develop a method to compute -conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accompli…
math.NA2024
Extended Galerkin neural network approximation of singular variational problems with error control
Mark Ainsworth, Justin Dong
We present extended Galerkin neural networks (xGNN), a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of…