In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

In this paper we propose a method for the finite element solution of elliptic interface problem,
using an approach due to Nitsche. The method allows for discontinuities, internal to the …

This paper is concerned with the analysis of a finite element method for nonhomogeneous
second order elliptic interface problems on smooth domains. The method consists in …

This article presents new immersed finite element (IFE) methods for solving the popular
second order elliptic interface problems on structured Cartesian meshes even if the involved …

A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-
structured interface-fitted mesh in two and three dimensions quickly is developed in this …

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 …

We analyze higher order finite elements applied to second order elliptic interface problems.
Our a priori error estimates in the L2-and H1-norm are expressed in terms of the …

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve
discontinuous-coefficient elliptic interface problems whose solution is continuous but has …

In this paper we present a new approach to simulations on complex‐shaped domains. The
method is based on a discontinuous Galerkin (DG) method, using trial and test functions …

In this article an unfitted discontinuous Galerkin method is proposed to discretize elliptic
interface problems. The method is based on the symmetric interior penalty discontinuous …