We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods
to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin …

We develop the Randomized Neural Networks with Petrov-Galerkin Methods (RNN-PG
methods) to solve linear elasticity problems. RNN-PG methods use Petrov-Galerkin …

The Brinkman equations can be regarded as a combination of the Stokes and Darcy
equations which model transitions between the fast flow in channels (governed by Stokes …

Combining the mixed discontinuous Galerkin method for the Darcy flow and the interior
penalty discontinuous Galerkin methods for the Stokes problem, a locally conservative …

Many stable and convergent numerical methods are not pressure robust for an
incompressible flow problem, due to the relaxation of a discrete divergence constraint called …

We study a mixed discontinuous Galerkin (DG) method for solving the second-order wave
equation. The stress variable p and the displacement variable u are discretized by the mixed …

In this paper, we introduce and analyze an augmented mixed discontinuous Galerkin (MDG)
method for a class of quasi-Newtonian Stokes flows. In the mixed formulation, the unknowns …

In this paper, we study the numerical solution of Darcy flow via a mixed discontinuous
Galerkin method. The two-step Euler backward formula is used for the time variable …

This paper presents a weak Galerkin (WG) finite element method for linear elasticity on
general polygonal and polyhedral meshes, free from convexity constraints, by leveraging …

A strongly symmetric stress approximation is proposed for the Brinkman equations with
mixed boundary conditions. The resulting formulation solves for the Cauchy stress using a …