In recent years, polygonal and polyhedral finite elements have gained much interest from
researchers as an alternative approach for discretizing complicated domains. Findings to …

We propose and analyze a local projection stabilization virtual element method for time-
fractional Burgers equation on polygonal meshes, whose solutions display a weak …

This paper introduces a general recovery-based a posteriori error estimation framework for
the Virtual Element Method (VEM) of arbitrary order on general polygonal/polyhedral …

This paper introduces a new numerical approach that integrates local randomized neural
networks (LRNNs) and the hybridized discontinuous Petrov–Galerkin (HDPG) method for …

In this paper, we develop an efficient virtual element method to solve the two-dimension time
fractional convection diffusion reaction equation involving the Caputo fractional derivative …

A refined a priori error analysis of the lowest-order (linear) nonconforming virtual element
method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D …

We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach for
modeling Raman gain in fiber laser amplifiers. In contrast with popular beam propagation …

We present a Trefftz-type finite element method on meshes consisting of curvilinear
polygons. Local basis functions are computed using integral equation techniques that allow …

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is
a method that is in some sense dual to the discontinuous Petrov–Galerkin (DPG) method …

Virtual element method is a new promising finite element method using general polygonal
meshes. Its optimal a priori error estimates are well established in the literature. In this …