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We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…

Numerical Analysis · Mathematics 2017-10-19 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov , Paolo Zunino

We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed…

Numerical Analysis · Mathematics 2024-01-03 L. Beirão da Veiga , F. Dassi , G. Vacca

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

Analysis of PDEs · Mathematics 2016-04-13 Fabian Christowiak , Carolin Kreisbeck

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the…

Numerical Analysis · Mathematics 2019-02-26 Fei Wang , Shuonan Wu , Jinchao Xu

In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…

Numerical Analysis · Mathematics 2022-03-14 Pei Cao , Jinru Chen , Feng Wang

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

We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…

Numerical Analysis · Mathematics 2020-09-10 August Johansson , Mats G. Larson , Anders Logg

The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…

Numerical Analysis · Mathematics 2010-01-12 Long Chen , Michael Holst , Jinchao Xu

We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…

Numerical Analysis · Mathematics 2019-10-31 Arzhang Angoshtari

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

We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…

Numerical Analysis · Mathematics 2025-11-26 Ben S. Ashby , Gabriel R. Barrenechea , Alex Lukyanov , Tristan Pryer , Alex Trenam

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

Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…

Materials Science · Physics 2008-04-17 Francois Willot , Yves-Patrick Pellegrini , Pedro Ponte Castaneda

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

Numerical Analysis · Mathematics 2018-09-21 Nicola A. Nodargi

This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method…

Numerical Analysis · Mathematics 2022-12-26 Wietse M. Boon , Alessio Fumagalli , Anna Scotti

We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…

Numerical Analysis · Mathematics 2026-05-20 Alexander Humer , Ivo Steinbrecher , Astrid Pechstein

This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…

Numerical Analysis · Mathematics 2022-10-04 Xiaobing Feng , Yukun Li , Yujian Lin

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

Numerical Analysis · Mathematics 2012-05-22 Lijian Jiang , Dylan Copeland , J. David Moulton

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

In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…

Numerical Analysis · Mathematics 2021-09-30 Santiago Badia , Alberto F. Martín , Francesc Verdugo