Abstract The Shifted Boundary Method (SBM) is an approximate domain method for
boundary value problems, in the broader class of unfitted/embedded/immersed methods …

An unfitted interface penalty finite element method (UIPFEM) is proposed for the elliptic
interface problems, in which Nitsche's method together with the ideas of merging elements …

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps)
by Massarwi and Elber in 2016, in this paper we present a novel approach for the …

We design and analyze a hybrid high-order (HHO) method on unfitted meshes to
approximate elliptic interface problems. The curved interface can cut through the mesh cells …

In this paper we study parametric trace finite element (TraceFEM) and parametric surface
finite element (SFEM) discretizations of a surface Stokes problem. These methods are …

We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to
approximate elliptic interface problems by means of a consistent penalty method à la …

Solving partial differential equations (PDE) on evolving geometries is a challenging and
useful task. The geometry that has to be treated in applications is often quite complicated …

An hp version of interface penalty finite element method (hp-IPFEM) is proposed to solve the
elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates …

In this paper, we study arbitrary order extended finite element (XFE) methods based on two
discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and …

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 …