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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…

Numerical Analysis · Mathematics 2015-05-05 August Johansson , Mats G. Larson , Anders Logg

We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…

Numerical Analysis · Mathematics 2021-09-27 Daniele Antonio Di Pietro , Ilaria Fontana , Kyrylo Kazymyrenko

We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the…

Numerical Analysis · Mathematics 2024-04-16 Rodolfo Araya , Alfonso Caiazzo , Franz Chouly

We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of…

Numerical Analysis · Mathematics 2023-07-24 Idrissa Niakh , Guillaume Drouet , Virginie Ehrlacher , Alexandre Ern

We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…

Numerical Analysis · Mathematics 2026-01-13 Tom Gustafsson , Antti Hannukainen , Vili Kohonen , Juha Videman

A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…

Numerical Analysis · Mathematics 2018-04-03 Simon Sticko , Gustav Ludvigsson , Gunilla Kreiss

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…

Numerical Analysis · Mathematics 2022-06-24 Xuehai Huang , Chao Zhang

We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming $C^1$-continuous finite elements. We implement the…

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

This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy…

Numerical Analysis · Mathematics 2022-08-12 Hailong Guo , Xu Yang

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…

Numerical Analysis · Mathematics 2026-05-19 Aparna Bansal , Nicolas A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

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

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

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

In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimates are analyzed under a low regularity condition, and the…

Numerical Analysis · Mathematics 2022-12-27 Yanjun Li , Hai Bi

In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two…

Classical Physics · Physics 2013-05-27 Serge Dumont , Frédéric Lebon , Raffaella Rizzoni

In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the…

Numerical Analysis · Mathematics 2018-08-15 Susanne Claus , Samuel Bigot , Pierre Kerfriden

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…

Numerical Analysis · Mathematics 2018-07-27 Thomas Ludescher , Sven Gross , Arnold Reusken

In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…

Numerical Analysis · Mathematics 2023-12-19 Arbaz Khan , Felipe Lepe , David Mora , Jesus Vellojin

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly-imposed Dirichlet boundary conditions using polynomial B-splines.

Numerical Analysis · Mathematics 2018-12-21 Ibrahim Al Balushi