The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

We introduce a Robust version of the Variational Physics-Informed Neural Networks method
(RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov …

A unified construction of high order shape functions is given for all four classical energy
spaces (H 1, H (curl), H (div) and L 2) and for elements of “all” shapes (segment …

This study presents an analytical framework based on the third-order shear deformation
theory (TSDT) to conduct a comprehensive thermo-vibro-acoustic evaluation of a multi …

Residual minimization is a widely used technique for solving Partial Differential Equations in
variational form. It minimizes the dual norm of the residual, which naturally yields a saddle …

We introduce the concept of machine-learning minimal-residual (ML-MRes) finite element
discretizations of partial differential equations (PDEs), which resolve quantities of interest …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

The phase field method is becoming the de facto choice for the numerical analysis of
complex problems that involve multiple initiating, propagating, interacting, branching and …

We introduce a space-time discretization for linear first-order hyperbolic evolution systems
using a discontinuous Galerkin approximation in space and a Petrov–Galerkin scheme in …

6.1▪“When All Else Fails, Integrate by Parts”: New and Old Variational Formulations for
Linear Elliptic PDEs 6.1. 1▪ Introduction Although the motto “when all else fails, integrate by …