We present a numerical approximation of Darcy's flow through a fractured porous medium
which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we …

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 …

Abstract Isogeometric Analysis (IgA) uses the same class of basis functions for both
representing the geometry of the computational domain and approximating the solution of …

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 …

The Stokes equation posed on surfaces is important in some physical models, but its
numerical solution poses several challenges not encountered in the corresponding …

We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on
a hypersurface embedded in. The method is constructed by using a discontinuous …

We consider a finite element method for Partial Differential Equations (PDEs) on surfaces.
Unlike many previous techniques, this approach is based on a geometrically intrinsic …

High-order spatial discretizations and full discretizations of parabolic partial differential
equations on evolving surfaces are studied. We prove convergence of the high-order …

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element
Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial …

We develop a finite element method for the Laplace–Beltrami operator on a surface with
boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a …