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In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

Numerical Analysis · Mathematics 2021-01-19 Xiaoxiao He , Fei Song , Weibing Deng

We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element…

Numerical Analysis · Mathematics 2026-05-01 Tom Gustafsson , Antti Hannukainen , Vili Kohonen , Juha Videman

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…

Numerical Analysis · Mathematics 2024-05-21 Tom Gustafsson , Juha Videman

We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…

Numerical Analysis · Mathematics 2012-05-30 André Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in…

Numerical Analysis · Mathematics 2020-07-02 Tom Gustafsson , Rolf Stenberg , Juha Videman

We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…

Numerical Analysis · Mathematics 2024-11-20 R. H. Drebotiy , H. A. Shynkarenko

We present a mixed finite element method with triangular and parallelogram meshes for the Kirchhoff-Love plate bending model. Critical ingredient is the construction of low-dimensional local spaces and appropriate degrees of freedom that…

Numerical Analysis · Mathematics 2024-05-30 Thomas Führer , Norbert Heuer

We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…

Numerical Analysis · Mathematics 2017-10-11 Peter Hansbo , Mats G. Larson , Andre Massing

We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…

Numerical Analysis · Mathematics 2022-06-27 Baiju Zhang , Zhimin Zhang

In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…

Numerical Analysis · Mathematics 2018-10-29 Erik Burman , Mihai Nechita , Lauri Oksanen

We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…

Numerical Analysis · Mathematics 2015-11-10 Erik Burman , Peter Hansbo , Mats G. Larson , Sara Zahedi

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…

Numerical Analysis · Mathematics 2019-02-05 Peter Hansbo , Mats G. Larson , Karl Larsson

We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We…

Numerical Analysis · Mathematics 2015-03-20 Peter Hansbo , Mats G. Larson , Sara Zahedi

We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…

Numerical Analysis · Mathematics 2025-03-13 Erik Burman , Lauri Oksanen , Ziyao Zhao

Optimal a priori and a posteriori error estimates are derived for Nitsche's mortar finite elements. The analysis is based on the equivalence of the Nitsche's method and the stabilised mixed method. The Nitsche's method is defined so that it…

Numerical Analysis · Mathematics 2021-02-09 Tom Gustafsson , Rolf Stenberg , Juha Videman

We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces.…

Numerical Analysis · Mathematics 2017-06-06 Erik Burman , Peter Hansbo , Mats G. Larson

This paper focusses on the von K\'{a}rm\'{a}n equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilinear fourth-order obstacle problem and motivates its…

Numerical Analysis · Mathematics 2020-09-08 Carsten Carstensen , Sharat Gaddam , Neela Nataraj , Amiya K Pani , Devika Shylaja

In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…

Numerical Analysis · Mathematics 2024-06-13 David Mora , Jesus Vellojin , Nitesh Verma

We consider a stabilized finite element method for the Darcy problem on a surface based on the Masud-Hughes formulation. A special feature of the method is that the tangential condition of the velocity field is weakly enforced through the…

Numerical Analysis · Mathematics 2015-11-13 Peter Hansbo , Mats G. Larson

In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…

Numerical Analysis · Mathematics 2015-07-14 Erik Burman , Peter Hansbo , Mats G. Larson