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In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order…

Numerical Analysis · Mathematics 2017-03-17 Mirza Cenanovic , Peter Hansbo , Mats G. Larson

In this paper, we design two classes of stabilized mixed finite element methods for linear elasticity on simplicial grids. In the first class of elements, we use $\boldsymbol{H}(\mathbf{div}, \Omega; \mathbb{S})$-$P_k$ and…

Numerical Analysis · Mathematics 2016-10-28 Long Chen , Jun Hu , Xuehai Huang

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…

Soft Condensed Matter · Physics 2016-05-05 Andrew DeBenedictis , Timothy J Atherton

We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…

Numerical Analysis · Mathematics 2019-10-22 Arzhang Angoshtari , Ali Gerami Matin

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…

Numerical Analysis · Mathematics 2020-07-30 Qingguo Hong , Chunmei Liu , Jinchao Xu

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…

Numerical Analysis · Mathematics 2023-08-16 Zhiming Chen , Yong Liu

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…

Numerical Analysis · Mathematics 2021-06-07 Kevin Tolle , Nicole Marheineke

A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the…

Materials Science · Physics 2017-11-16 Emilio Martínez-Pañeda , Christian F. Niordson , Lorenzo Bardella

This study presents the analytical and finite element formulation of a geometrically nonlinear and fractional-order nonlocal model of an Euler-Bernoulli beam. The finite nonlocal strains in the Euler-Bernoulli beam are obtained from a…

Numerical Analysis · Mathematics 2020-06-22 Sai Sidhardh , Sansit Patnaik , Fabio Semperlotti

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…

Numerical Analysis · Mathematics 2023-05-01 Stefan Frei , Gozel Judakova , Thomas Richter

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…

Numerical Analysis · Mathematics 2020-04-02 Evgenija D. Popova

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…

Numerical Analysis · Mathematics 2025-10-21 Xiaowen Gan , Yuqian Teng , Sisheng Wang

A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…

Numerical Analysis · Mathematics 2026-04-16 Lutz Angermann

The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…

Numerical Analysis · Mathematics 2018-05-02 August Johansson , Mats G. Larson , Anders Logg

We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…

Numerical Analysis · Mathematics 2024-11-20 R. H. Drebotiy , H. A. Shynkarenko

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…

Numerical Analysis · Mathematics 2026-05-12 Patrick Bammer , Lothar Banz , Miriam Schönauer , Andreas Schröder

We develop a discontinuous cut finite element method (CutFEM) for the Laplace-Beltrami operator on a hypersurface embedded in $\mathbb{R}^d$. The method is constructed by using a discontinuous piecewise linear finite element space defined…

Numerical Analysis · Mathematics 2015-07-22 Erik Burman , Peter Hansbo , Mats G. Larson , Andre Massing

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…

Optimization and Control · Mathematics 2021-04-19 Duy Phan , Lassi Paunonen