Related papers: Removing the stabilization parameter in fitted and…
The full Stokes equations are solved by a finite element method for simulation of large ice sheets and glaciers. The simulation is particularly sensitive to the discretization of the grounding line which separates the ice resting on the…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…
We introduce a new general framework for the approximation of evolution equations at low regularity and develop a new class of schemes for a wide range of equations under lower regularity assumptions than classical methods require. In…
In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…
We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CG-HDG coupling exploits the…
We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and convergence for arbitrary order finite element interpolation…
In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…
We consider the asymptotically flat standing wave solutions to the Poisson-Schr\"{o}dinger system of equations known as static states. These solutions can be parameterized using a variety of choices of two continuous parameters and one…
In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…
The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
In this paper we consider a class of unfitted finite element methods for scalar elliptic problems. These so-called CutFEM methods use standard finite element spaces on a fixed unfitted triangulation combined with the Nitsche technique and a…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
We introduce the cut finite element method in the language of finite element exterior calculus, by formulating a stabilisation -- for any form degree -- that makes the method robust with respect to the position of the interface relative to…
In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general…