This review paper discusses the developments in immersed or unfitted finite element
methods over the past decade. The main focus is the analysis and the treatment of the …

The review of the optimal local truncation error method (OLTEM) for the numerical solution of
PDEs is presented along with some new developments of OLTEM. First, we explain the …

Fractures have attracted the attention of computational scientists for several decades. The
modeling and simulation of fractures have been a major motivation for developing enriched …

In this article, we study the effect of small-cut elements on the critical time-step size in an
immersogeometric explicit dynamics context. We analyze different formulations for second …

In this work, we propose a novel formulation for the solution of partial differential equations
using finite element methods on unfitted meshes. The proposed formulation relies on the …

The unstable nature of the material point method (MPM) is widely documented and is a
barrier to the method being used for routine engineering analyses of large deformation …

We consider the reliable implementation of high-order unfitted finite element methods on
Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable …

When modeling scientific and industrial problems, geometries are typically modeled by
explicit boundary representations obtained from computer-aided design software. Unfitted …

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with
application to steady heat conduction and viscous flow problems. The proposed strategy is …

The numerical manifold method (NMM) has been widely utilized to solve problems involving
complicated boundaries, cracks, and interfaces. Recently, strain or gradient smoothing …