This article outlines the research on the application of the variational multiscale theory
(VMS) to a posteriori error estimation. VMS theory was initially developed by Professor …

The primary objective of this work is to extend the capability of the arbitrary Lagrangian–
Eulerian (ALE)‐based strategy for solving fluid–structure interaction problems. This is driven …

A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the
incompressible Navier–Stokes equations is presented. The key ingredient is an accurate …

We present a general formulation for incompressible fluid flow analysis using the finite
element method (FEM). The standard Eulerian formulation is described first. The necessary …

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 …

This paper presents an explicit a-posteriori error estimator for the multi-dimensional
transport equation based on an approximation to the variational multiscale theory. The …

As the finite element method requires many nodes or elements to obtain accurate results,
the adaptive finite element method has been developed to obtain better results with fewer …

A new explicit a-posteriori error estimator is investigated, which emanates from the
variational multiscale theory. The error estimator uses an approximation of the Green's …

Fixed‐grid methods for moving interface problems offer a number of attractive properties and
have therefore gained quite some popularity in recent time. However, moving mesh …

This paper extends explicit a posteriori error estimators based on the variational multiscale
theory to systems of equations. In particular, the emphasis is placed on flow problems: the …