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In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…

Numerical Analysis · Mathematics 2025-10-08 Nicolás A. Barnafi , Felipe Lepe , Francisca Muñoz Riquelme

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

This paper is devoted to study the Arnold-Winther mixed finite element method for two dimensional Stokes eigenvalue problems using the stress-velocity formulation. A priori error estimates for the eigenvalue and eigenfunction errors are…

Numerical Analysis · Mathematics 2017-12-20 Joscha Gedicke , Arbaz Khan

We define a finite element method for the coupling of Stokes and nonlinear Poisson--Boltzmann equations. The novelty in the formulation is that the coupling from the electric potential to the drag in the momentum balance is rewritten as a…

Numerical Analysis · Mathematics 2026-03-11 Abeer F. AlSohaim , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…

Numerical Analysis · Mathematics 2025-03-12 Jorge Aguayo Araneda , Julie Merten

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

Numerical Analysis · Mathematics 2018-06-15 Arbaz Khan , Catherine E. Powell , David J. Silvester

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…

Numerical Analysis · Mathematics 2020-03-17 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…

Numerical Analysis · Mathematics 2013-10-23 Bishnu P. Lamichhane

We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…

Numerical Analysis · Mathematics 2015-05-05 August Johansson , Mats G. Larson , Anders Logg

In this article, we analyze a two-level finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse…

Numerical Analysis · Mathematics 2021-07-09 Deepjyoti Goswami , Pedro D. Damázio

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming…

Numerical Analysis · Mathematics 2015-06-04 Seungwoo Lee , Do Y. Kwak , Imbo Sim

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

For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is…

Numerical Analysis · Mathematics 2020-06-05 Xuefeng Liu , Mitsuhiro Nakao , Chun'guang You , Shin'ichi Oishi

Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a…

Numerical Analysis · Mathematics 2022-09-20 Seshadri R. Basava , Winnifried Wollner

The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…

Numerical Analysis · Mathematics 2025-12-16 Michael Neilan , Maxim Olshanskii , Henry von Wahl

An optimal and robust low-order nonconforming finite element method is developed for the strain gradient elasticity (SGE) model in arbitrary dimension. An $H^2$-nonconforming quadratic vector-valued finite element in arbitrary dimension is…

Numerical Analysis · Mathematics 2025-12-30 Jianguo Huang , Xuehai Huang , Zheqian Tang

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

Numerical Analysis · Mathematics 2023-01-16 Erik Burman , Deepika Garg , Janosch Preuss

In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimates are analyzed under a low regularity condition, and the…

Numerical Analysis · Mathematics 2022-12-27 Yanjun Li , Hai Bi

In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under…

Numerical Analysis · Mathematics 2015-07-01 Gouranga Mallik , Neela Nataraj

We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are…

Numerical Analysis · Mathematics 2013-10-30 Lars Diening , Christian Kreuzer , Endre Süli