We propose and analyze a discontinuous finite element method for nearly incompressible
linear elasticity on triangular meshes. We show optimal error estimates that are uniform with …

This paper aims at a general guideline to obtain a posteriori error estimates for the finite
element error control in computational partial differential equations. In the abstract setting of …

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 …

In this work, we study numerical issues related to a common mathematical model which
describes ferromagnetic materials, both in a stationary and nonstationary context …

Residual-based a posteriori error estimates were derived within one unifying framework for
lowest-order conforming, nonconforming, and mixed finite element schemes in Carstensen …

An adaptive discontinuous Galerkin finite element method for linear elasticity problems is
presented. We develop an a posteriori error estimate and prove its robustness with respect …

Residual-based a posteriori error estimates are derived within a unified setting for lowest-
order conforming, nonconforming, and mixed finite element schemes. The various residuals …

In this paper, we solve the coupled Ginzburg-Landau equations by using a linearized
variable-time-step second order backward differentiation formula in time combining with a …

Computable a posteriori error bounds and related adaptive mesh-refining algorithms are
provided for the numerical treatment of monotone stationary flow problems with a quite …

We present two kinds of lowest-order virtual element methods for planar linear elasticity
problems. For the first one we use the nonconforming virtual element method with a …