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The damping of built-up structures stems largely from the microscopic dry frictional interactions in the contact interfaces. The accurate prediction of friction damping has been an important scientific aim of the past several decades.…

Systems and Control · Electrical Eng. & Systems 2025-07-17 Hendrik D. Linder , Johann Gross , Malte Krack

For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…

Numerical Analysis · Mathematics 2022-09-19 J. Gwinner , N. Ovcharova

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

We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {\ttfamily deal.II} library. It addresses both high-order…

Numerical Analysis · Mathematics 2024-08-12 Nils Margenberg , Peter Munch

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

Numerical Analysis · Mathematics 2016-11-01 Daniel Elfverson , Mats G. Larson , Axel Målqvist

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…

Numerical Analysis · Mathematics 2021-03-05 Stefan Takacs

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…

Numerical Analysis · Mathematics 2024-09-11 Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…

Numerical Analysis · Mathematics 2021-12-28 Fanyi Yang , Xiaoping Xie

We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We…

Numerical Analysis · Mathematics 2021-12-30 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…

Numerical Analysis · Mathematics 2022-03-16 Chiu Ling Chan , Felix Scholz , Thomas Takacs

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

We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…

Numerical Analysis · Mathematics 2026-04-02 Peter Gangl , Ulrich Langer

In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…

Numerical Analysis · Mathematics 2026-01-21 M. Saberi , A. Vogel

Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…

Numerical Analysis · Mathematics 2023-02-08 Rutger A. Biezemans , Claude Le Bris , Frederic Legoll , Alexei Lozinski

When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the…

Computational Engineering, Finance, and Science · Computer Science 2024-06-06 Jedrzej Dobrzanski , Kajetan Wojtacki , Stanislaw Stupkiewicz

In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre…

Numerical Analysis · Mathematics 2025-09-18 Nuo Lei , Donghang Zhang , Weiying Zheng

We analyze a finite element/boundary element procedure to solve a non-convex contact problem for the double-well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain…

Numerical Analysis · Mathematics 2010-09-16 Heiko Gimperlein , Matthias Maischak , Elmar Schrohe , Ernst P. Stephan

This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points…

Computational Physics · Physics 2020-06-16 Herbert De Gersem , Armin Galetzka , Ion Gabriel Ion , Dimitrios Loukrezis , Ulrich Römer

In this paper, we propose a stabilised finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction--free contact, but the formulation is…

Numerical Analysis · Mathematics 2017-11-15 Erik Burman , Peter Hansbo , Mats G. Larson

We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…

Numerical Analysis · Mathematics 2022-05-11 Dmitri Kuzmin , Jan-Phillip Bäcker