This paper aims first at a simultaneous axiomatic presentation of the proof of optimal
convergence rates for adaptive finite element methods and second at some refinements of …

Sparse matrixlization, an innovative programming style for MATLAB, is introduced and used
to develop an efficient software package, iFEM, on adaptive finite element methods. In this …

In this paper, we systematically review interface-driven mesh adaptation procedures for the
phase-field modeling of fluid–structure interaction problems. One of the popular ways of …

This is a survey of the theory of adaptive finite element methods (AFEMs), which are
fundamental to modern computational science and engineering but whose mathematical …

We propose an effective and flexible way to assemble finite element stiffness and mass
matrices in MATLAB. The major loops in the code have been vectorized using the so called …

We propose an effective and flexible way to assemble finite element stiffness and mass
matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical …

This introductory chapter on the mathematical theory of finite element methods (FEMs)
discusses its h-version for elliptic boundary value problems in the displacement formulation …

The paper presents an adaptive analysis within the framework of the node‐based smoothed
finite element method (NS‐FEM) using triangular elements. An error indicator based on the …

In the present paper we initiate the challenging task of building a mathematically sound
theory for adaptive virtual element methods (AVEMs). Among the realm of polygonal …

In this paper we present a new adaptive two-stage algorithm for solving elliptic partial
differential equations via a radial basis function collocation method. Our adaptive meshless …