Related papers: Projected gradient stabilization of sharp and diff…
We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set…
In the recent paper [C. Lehrenfeld, A. Reusken, SIAM J. Num. Anal., 51 (2013)] a new finite element discretization method for a class of two-phase mass transport problems is presented and analyzed. The transport problem describes mass…
A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band around the interface. An extension procedure, which is essential…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…
This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
In this note, we develop a new stabilization mechanism for cut finite element methods that generalizes previous approaches of ghost penalty type in two ways: (1) The quantity that is stabilized and (2) The choice of elements that are…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…
In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
We prove an optimal error estimate for the flux variable for a stabilized unfitted Nitsche finite element method applied to an elliptic interface problem with discontinuous constant coefficients. Our result shows explicitly that this error…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…
In many situations with finite element discretizations it is desirable or necessary to impose boundary or interface conditions not as essential conditions -- i.e. through the finite element space -- but through the variational formulation.…
In this paper we consider a class of fictitious domain finite element methods known from the literature. These methods use standard finite element spaces on a fixed unfitted triangulation combined with the Nitsche technique and a ghost…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…
We propose a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh. The dependent variables of velocity, pressure…