Quasi-optimal $hp$-finite element refinements towards singularities via deep neural network prediction

no code implementations • 13 Sep 2022 • Tomasz Sluzalec, Rafal Grzeszczuk, Sergio Rojas, Witold Dzwinel, Maciej Paszynski

We aim to construct the DNN expert to identify quasi-optimal $hp$ refinements of the coarse mesh elements.

Projection in negative norms and the regularization of rough linear functionals

no code implementations • 8 Jan 2021 • Felipe Millar, Ignacio Muga, Sergio Rojas, Kristoffer G. Van der Zee

We focus on projections onto discrete finite element spaces $G_n$, and consider both discontinuous as well as continuous piecewise-polynomial approximations.

Numerical Analysis Numerical Analysis