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Related papers: Nitsche's method for unilateral contact problems

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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

A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates,…

Numerical Analysis · Mathematics 2018-08-15 Qingyuan Hu , Franz Chouly , Ping Hu , Gengdong Cheng , Stéphane Pierre Alain Bordas

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

In this article, a reliable and efficient a posteriori error estimator of residual type is derived for a class of discontinuous Galerkin methods for the frictional contact problem with reduced normal compliance which is modeled as a…

Numerical Analysis · Mathematics 2021-04-19 Kamana Porwal , Tanvi

In this article, we present various numerical methods to solve multi-contact problems within the Non-Smooth Discrete Element Method. The techniques considered to solve the frictional unilateral conditions are based both on the bi-potential…

Numerical Analysis · Mathematics 2012-04-27 Serge Dumont

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 consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…

Numerical Analysis · Mathematics 2024-12-02 Sergio Caucao , Paulo Zúñiga

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 consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…

Numerical Analysis · Mathematics 2025-03-31 T. Chaumont-Frelet

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

The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…

Numerical Analysis · Mathematics 2016-08-30 Alejandro Allendes , Enrique Otarola , Richard Rankin , Abner J. Salgado

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related…

Numerical Analysis · Mathematics 2022-02-23 Andrea Franceschini , Matteo Frigo , Carlo Janna , Massimiliano Ferronato

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…

Numerical Analysis · Mathematics 2016-01-20 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully…

Numerical Analysis · Mathematics 2023-05-01 Amy de Castro , Hyesuk Lee , Margaret M. Wiecek

We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…

Numerical Analysis · Mathematics 2025-10-03 Najwa Alshehri , Daniele Boffi , Fabio Credali , Lucia Gastaldi

This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary…

Numerical Analysis · Mathematics 2025-08-13 Jun Hu , Rui Ma , Min Zhang

In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…

Numerical Analysis · Mathematics 2007-05-23 Laurent Baillet , Taoufik Sassi

This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…

Numerical Analysis · Mathematics 2026-02-24 Yuwen Li , Han Shui

In this paper we will discuss different coupling methods {suitable for use in} the framework of the recently introduced CutFEM paradigm, cf. Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, Andr\'e . CutFEM:…

Numerical Analysis · Mathematics 2017-02-28 Erik Burman , Peter Hansbo

In this paper we discuss a hybridised method for FEM-BEM coupling. The coupling from both sides use a Nitsche type approach to couple to the trace variable. This leads to a formulation that is robust and flexible with respect to…

Numerical Analysis · Mathematics 2022-03-22 Timo Betcke , Michał Bosy , Erik Burman