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 …

We develop a theoretical framework for the analysis of stabilized cut finite element methods
for the Laplace-Beltrami operator on a manifold embedded in ℝ d of arbitrary codimension …

In this contribution we present a new computational method for coupled bulk-surface
problems on time-dependent domains. The method is based on a space–time formulation …

This paper shows an inf-sup stability property for several well-known 2D and 3D Stokes
elements on triangulations which are not fitted to a given smooth or polygonal domain. The …

Partial differential equations posed on surfaces arise in a number of applications. In this
survey we describe three popular finite element methods for approximating solutions to the …

Stationary and instationary Stokes and Navier‐Stokes flows are considered on two‐
dimensional manifolds, ie, on curved surfaces in three dimensions. The higher‐order …

In the context of unfitted finite element discretizations, the realization of high-order methods
is challenging due to the fact that the geometry approximation has to be sufficiently accurate …

We present a new high-order finite element method for the discretization of partial differential
equations on stationary smooth surfaces which are implicitly described as the zero level of a …

In this paper we consider a class of unfitted finite element methods for discretization of
partial differential equations on surfaces. In this class of methods known as the Trace Finite …

In this article we present a new implicit numerical scheme for reaction–diffusion–advection
equations on an evolving in time hypersurface Γ (t). The partial differential equations are …