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In this note we show that the non-symmetric version of the classical Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. We prove optimal $H^1$-error estimates and $L^2$-estimates that are…

Numerical Analysis · Mathematics 2011-11-07 Erik Burman

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

We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method is…

Numerical Analysis · Mathematics 2016-09-14 Erik Burman , Peter Hansbo , Mats G. Larson

In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure…

Numerical Analysis · Mathematics 2023-11-28 Hailong Guo , Mingyan Zhang , Qian Zhang , Zhimin Zhang

In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the $H^1$- and…

Numerical Analysis · Mathematics 2015-07-28 Thomas Boiveau , Erik Burman

We propose a stabilized Nitsche-based cut finite element formulation for the Oseen problem in which the boundary of the domain is allowed to cut through the elements of an easy-to-generate background mesh. Our formulation is based on the…

Numerical Analysis · Mathematics 2017-03-30 Andre Massing , Benedikt Schott , Wolfgang A. Wall

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite…

Numerical Analysis · Mathematics 2019-12-17 Frits de Prenter , Christoph Lehrenfeld , André Massing

Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element…

Computational Engineering, Finance, and Science · Computer Science 2020-01-30 Nathan Sime , Cian R. Wilson

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

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…

Numerical Analysis · Mathematics 2022-07-13 Fanyi Yang , Xiaoping Xie

Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival owing to its natural application in modern computational…

Numerical Analysis · Mathematics 2025-05-13 Hiroki Ishizaka

We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell…

Numerical Analysis · Mathematics 2022-03-17 Karl Larsson , Stefan Kollmannsberger , Ernst Rank , Mats G. Larson

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

Numerical Analysis · Mathematics 2017-07-05 Ramona Baumann , Thomas P. Wihler

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

Numerical Analysis · Mathematics 2022-04-21 Oded Stein , Eitan Grinspun , Alec Jacobson , Max Wardetzky

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

Numerical Analysis · Mathematics 2018-01-03 Peter Hansbo , Tobias Jonsson , Mats G. Larson , Karl Larsson

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…

Numerical Analysis · Mathematics 2015-02-23 Erik Burman , Susanne Claus , André Massing

We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties…

Numerical Analysis · Mathematics 2025-08-18 Cu Cui , Guido Kanschat

The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…

Numerical Analysis · Mathematics 2018-03-28 Yuki Ueda , Norikazu Saito

We consider two methods for treating elastic contact problems with the finite element method; the penalty method and Nitsche's method. For the penalty method we discuss how the penalty parameter should be chosen. Both the theoretical…

Numerical Analysis · Mathematics 2025-05-29 Tom Gustafsson , Rolf Stenberg

We develop a Nitsche finite element method for a model of Euler--Bernoulli beams with axial stiffness embedded in a two--dimensional elastic bulk domain. The beams have their own displacement fields, and the elastic subdomains created by…

Numerical Analysis · Mathematics 2022-03-02 Peter Hansbo , Mats G. Larson
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