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math.NA2022
A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis
We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds a…
math.NA2022
Discrete Gradient Flow Approximations of High Dimensional Evolution Partial Differential Equations via Deep Neural Networks
Emmanuil H. Georgoulis, Michail Loulakis, Asterios Tsiourvas
We consider the approximation of initial/boundary value problems involving, possibly high-dimensional, dissipative evolution partial differential equations (PDEs) using a deep neur…