We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for
second-order elliptic partial differential equations, and a priori error estimates were …

This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

An interior-penalty discontinuous Galerkin (dG) method for an\penalty-10000 elliptic
interface problem involving, possibly, curved interfaces, with flux-\penalty-10000 balancing …

In this paper, we introduce adaptive network enhancement (ANE) method for the best least-
squares approximation using two-layer ReLU neural networks (NNs). For a given function f …

We study in this paper a posteriori error estimates for H 1-conforming numerical
approximations of diffusion problems with a diffusion coefficient piecewise constant on the …

For elliptic interface problems in two and three dimensions, this paper studies a priori and
residual-based a posteriori error estimations for the Crouzeix--Raviart nonconforming and …

In [Z. Cai and S. Zhang, SIAM J. Numer. Anal., 47 (2009), pp. 2132–2156], we introduced
and analyzed a recovery-based a posteriori error estimator for conforming linear finite …

Abstract In the companion paper [1], we introduce adaptive network enhancement (ANE)
method for the best least-squares approximation to a target function by using two-layer …

This article presents a computationally efficient and straightforward to implement a posteriori
error estimator for second‐order G/XFEM and FEM approximations. The formulation is …