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We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…

Numerical Analysis · Mathematics 2024-03-07 Zhiming Chen , Yong Liu

An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…

Numerical Analysis · Mathematics 2025-08-01 S. M. Mallikarjunaiah , Pavithra Venkatachalapthy

A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…

Optimization and Control · Mathematics 2014-11-19 L. Adam , J. V. Outrata , T. Roubicek

We show how the quasi-analytic method developed to solve linear elastic contacts to coated substrates (Perriot A. and Barthel E. {\em J. Mat. Res.}, {\bf 2004}, {\em 19}, 600) may be extended to adhesive contacts. Substrate inhomogeneity…

Classical Physics · Physics 2009-11-13 Etienne Barthel , Antoine Perriot

The exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are considered, provided that the materials of…

Mathematical Physics · Physics 2024-05-29 Nugzar Shavlakadze , Nana Odishelidze , Francisco Criado-Aldeanueva

The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…

Numerical Analysis · Mathematics 2014-02-14 Asha K. Dond , Neela Nataraj , Amiya K. Pani

This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…

Numerical Analysis · Mathematics 2025-11-04 Paolo Piersanti , Tianyu Sun

Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE…

Numerical Analysis · Mathematics 2022-05-25 Marco Pasetto , Zhaoxiang Shen , Marta D'Elia , Xiaochuan Tian , Nathaniel Trask , David Kamensky

A phase-field approach is proposed for interface failure between two possibly dissimilar materials. The discrete adhesive interface is regularised over a finite width. Due to the use of a regularised crack model for the bulk material, an…

Materials Science · Physics 2019-09-06 Arne Claus Hansen-Dörr , René de Borst , Paul Hennig , Markus Kästner

Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterized by the Young modulus varying with depth as a power function.…

Analysis of PDEs · Mathematics 2022-02-14 Y. A. Antipov , S. M. Mkhitaryan

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

Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…

Analysis of PDEs · Mathematics 2021-12-14 Christopher Brand , Georg Dolzmann , Alessandra Pluda

We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…

Analysis of PDEs · Mathematics 2025-09-19 Govanni Granados , Jeremy L. Marzuola , Casey Rodriguez

We propose a new nonconforming finite element method for solving Stokes interface problems. The method is constructed on local anisotropic mixed meshes, which are generated by fitting the interface through simple connection of intersection…

Numerical Analysis · Mathematics 2025-07-04 Geng Chenchen , Hua Wang , Fengren Zou

In the present paper we show that the normal contact problem between two elastic bodies in the halfspace approximation can always be transformed to an equivalent problem of the indentation of a profile into an elastic Winkler foundation.…

Soft Condensed Matter · Physics 2015-10-26 Valentin L. Popov , Roman Pohrt , Markus Heß

The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular…

Materials Science · Physics 2022-03-22 Solomon S. Melides , Dominic Vella , Marco Ramaioli

Since Hertz's pioneering work in 1882, contact mechanics traditionally grounds on linear elasticity, assuming small strains and displacements. However, recent experiments clearly highlighted linear elasticity limitations in accurately…

Soft Condensed Matter · Physics 2025-03-13 M. Ceglie , G. Violano , L. Afferrante , N. Menga

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

Numerical Analysis · Mathematics 2017-11-28 Eldar Khattatov , Ivan Yotov

Recently Guduru and coworkers have demonstrated with neat theory and experiments that both increase of strength and of toughness are possible in the contact of a rigid sphere with concentric single scale of waviness, against a very soft…

Materials Science · Physics 2016-03-03 M. Ciavarella

Interference-fit joints are typically adopted to produce permanent assemblies among mechanical parts. The resulting contact pressure is generally used for element fixing or to allow load transmission. Nevertheless, some special designs take…

Optics · Physics 2021-12-08 Luca Esposito , Alcide Bertocco , Matteo Bruno , Andrew Ruggiero