A unified study is presented in this paper for the design and analysis of different finite
element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs …

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 present a hybrid discontinuous Galerkin method for the velocity/stress formulation of
Zener's model in dynamic viscoelasticity. Our approach utilizes a spatial discretization that …

New low-order H (div)-conforming finite elements for symmetric tensors are constructed in
arbitrary dimension. The space of shape functions is defined by enriching the symmetric …

We present an abstract framework for the eigenvalue approximation of a class of non-
coercive operators. We provide sufficient conditions to guarantee the spectral correctness of …

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

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear
elasticity problem with arbitrary order discontinuous finite element spaces in d-dimension …

We propose and rigorously analyze a semi-and fully discrete discontinuous Galerkin method
for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic …

In this paper, we design two classes of stabilized mixed finite element methods for linear
elasticity on simplicial grids. In the first class of elements, we use 𝑯⁢(div, Ω; 𝕊)-P k and 𝑳 …

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 …