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The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…

Computational Physics · Physics 2018-06-05 Alexey Y. Chernyshenko , Maxim A. Olshanskii , Yuri V. Vassilevski

The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…

Numerical Analysis · Mathematics 2015-07-16 Thomas Carraro , Sven Wetterauer

This article's main scope is the presentation of a computational method for the simulation of contact problems within the finite element method involving complex and rough surfaces. The approach relies on the MPJR (eMbedded Profile for…

Soft Condensed Matter · Physics 2025-04-03 Jacopo Bonari , Marco Paggi , Daniele Dini

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…

Materials Science · Physics 2011-11-08 J. Novák , Ł. Kaczmarczyk , P. Grassl , J. Zeman , C. J. Pearce

A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…

Numerical Analysis · Mathematics 2007-07-12 Gunther H. Peichl , Rachid Touzani

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…

Numerical Analysis · Mathematics 2019-02-05 Peter Hansbo , Mats G. Larson , Karl Larsson

Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the…

Numerical Analysis · Mathematics 2013-09-06 Sundararajan Natarajan , Ean Tat Ooi , Irene Chiong , Chongmin Song

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

Graphics · Computer Science 2018-07-04 Silvia Sellán , Herng Yi Cheng , Yuming Ma , Mitchell Dembowski , Alec Jacobson

This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Gauss-Seidel, or conjugate gradient, with initial guess being…

Numerical Analysis · Mathematics 2026-05-07 Yuwen Li , Han Shui , Ludmil Zikatanov

In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…

Numerical Analysis · Mathematics 2025-11-27 Stefano Berrone , Lorenzo Neva , Moreno Pintore , Gioana Teora , Fabio Vicini

A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…

Numerical Analysis · Computer Science 2018-05-18 J. Poblet-Puig , A. V. Shanin

The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…

Numerical Analysis · Mathematics 2026-01-28 Eky Febrianto , Jakub Sistek , Pavel Kus , Matija Kecman , Fehmi Cirak

When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…

Computational Engineering, Finance, and Science · Computer Science 2024-05-24 Pere A. Martorell , Santiago Badia

We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on…

Numerical Analysis · Mathematics 2019-08-06 Ilona Ambartsumyan , Eldar Khattatov , Jan M. Nordbotten , Ivan Yotov

We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables.…

Numerical Analysis · Mathematics 2025-11-11 Wietse M. Boon , Alessio Fumagalli , Jan M. Nordbotten , Ivan Yotov

In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…

Numerical Analysis · Mathematics 2014-07-14 Sundararajan Natarajan , Chongmin Song , Salim Belouettar

We consider convection-diffusion problems in time-dependent domains and present a space-time finite element method based on quadrature in time which is simple to implement and avoids remeshing procedures as the domain is moving. The…

Numerical Analysis · Mathematics 2017-07-25 Sara Zahedi

Due to the limit of mesh density, the improvement of the spatial precision of numerical computation always leads to a decrease in computing efficiency. Aiming at this inability of numerical computation, we propose a novel method for…

Numerical Analysis · Mathematics 2021-04-05 Handing Xu , Zhenguo Nie , Qingfeng Xu , Xinjun Liu

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

Numerical Analysis · Computer Science 2011-07-20 Stephane PA Bordas , Sundararajan Natarajan

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…

Computational Engineering, Finance, and Science · Computer Science 2024-05-30 Abhiroop Satheesh , Christoph P. Schmidt , Wolfgang A. Wall , Christoph Meier