Partition of unity enrichment is known to significantly enhance the accuracy of the finite
element method by allowing the incorporation of known characteristics of the solution in the …

In this paper, we propose the extended virtual element method (X-VEM) to treat singularities
and crack discontinuities that arise in the Laplace problem. The virtual element method …

An improved XFEM (IXFEM) for three-dimensional linear elastic fracture mechanics (LEFM)
problems is developed. It utilizes an extra-dof free PU approximation to fundamentally …

This paper presents numerical studies with three classes of quadratic Generalized FEM
(GFEM) approximations and shows that all of them lead to errors that are orders of …

Abstract Generalized or Extended Finite Element Methods (GFEM/XFEM) of degree 1 for
interface problems have been reported in the literature; they (i) yield optimal order of …

This paper proposes a stable generalized finite element method (SGFEM) for the linear 3D
elasticity problem with cracked domains. Conventional material-independent branch …

In this paper, the quadratic Stable Generalized Finite Element Method (SGFEM) proposed in
Sanchez-Rivadeneira and Duarte (2019) is extended to 3-D fracture problems with non …

Interface problems have long been a major focus of scientific computing, leading to the
development of various numerical methods. Traditional mesh-based methods often employ …

In this paper, we propose a Strongly Stable generalized finite element method (SSGFEM) for
a non-smooth interface problem, where the interface has a corner. The SSGFEM employs …

Abstract The Hierarchical Interface-enriched Finite Element Method (HIFEM) is a technique
for solving problems containing discontinuities in the field gradient using finite element …