Since their emergence in the early 1950s, finite element methods have become one of the
most versatile and powerful methodologies for the approximate numerical solution of partial …

We investigate a novel method for the numerical solution of two-dimensional time-
dependent convection–diffusion–reaction equations with nonhomogeneous boundary …

This article concerns mesh restrictions that are needed to satisfy several important
mathematical properties—maximum principles, comparison principles, and the nonnegative …

Usually for the conventional numerical methods the increase of their accuracy and stability is
at the cost of increasing the size of the computational stencil. In the present work, without …

We present a robust computational framework for advective–diffusive–reactive systems that
satisfies maximum principles, the non-negative constraint, and element-wise species …

In the present work, a finite volume scheme (FVS) for simulating spatiotemporal patterns in
tubular reactors is proposed without increasing the size of the stencil of the classical finite …

In this paper, we introduce a least‐squares virtual element method for the convection‐
diffusion‐reaction problem in mixed form. We use the H (div) virtual element and continuous …

We propose an optical-fibre metal-insulator-metal (MIM) plasmonic sensor based on the
Fano resonances of surface plasmon polaritons (SPPs). Its structure consists of a coupling …

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS)
formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three …

This paper is devoted to the approximation of the convection–diffusion–reaction equation
using a mixed, first-order, formulation. We propose, and analyse, a stabilised finite element …