We discuss recent advances on robust unfitted finite element methods on cut meshes. These
methods are designed to facilitate computations on complex geometries obtained, for …

We introduce a new multiscale finite element method which is able to accurately capture
solutions of elliptic interface problems with high contrast coefficients by using only coarse …

A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper
for solving second order elliptic equations with discontinuous coefficients and interfaces …

We present a novel physics-informed neural networks (PINNs) framework for modeling
interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks …

Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and
accurate simulation of complex geometries by utilizing higher-order shape functions and an …

We develop both stable and stabilized methods for imposing Dirichlet constraints on
embedded, three‐dimensional surfaces in finite elements. The stable method makes use of …

We present a second order accurate, geometrically flexible and easy to implement method
for solving the variable coefficient Poisson equation with interfacial discontinuities or on …

Immersed finite element methods generally suffer from conditioning problems when cut
elements intersect the physical domain only on a small fraction of their volume. We present a …

We present a numerical method for the variable coefficient Poisson equation in three-
dimensional irregular domains and with interfacial discontinuities. The discretization …

A typical elliptic interface problem is casted as piecewise defined elliptic partial differential
equations (PDE) in different regions which are coupled together with interface conditions …