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The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress…

Numerical Analysis · Mathematics 2015-04-15 Jun Hu

This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…

Computational Engineering, Finance, and Science · Computer Science 2022-04-06 Bensingh Dhas , Jamun Kumar N , Debasish Roy , J N Reddy

In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics…

Numerical Analysis · Mathematics 2021-09-28 Zhihao Ge , Xiangzi Fu

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…

Numerical Analysis · Mathematics 2013-12-24 Amanda E. Diegel , Xiaobing H. Feng , Steven M. Wise

We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…

Numerical Analysis · Mathematics 2023-03-03 Sergio Caucao , Johann Esparza

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

Numerical Analysis · Mathematics 2025-06-24 Robert C. Kirby , John D. Stephens

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

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid…

Numerical Analysis · Mathematics 2014-07-03 Feiteng Huang , Xiaoping Xie , Chen-Song Zhang

In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…

Numerical Analysis · Mathematics 2026-02-24 Yanan He , Zhihao Ge

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces in multi-ply multi-directional composite laminates. In…

Computational Engineering, Finance, and Science · Computer Science 2020-08-21 Gourab Ghosh , Ravindra Duddu , Chandrasekhar Annavarapu

We propose a new nonconforming finite element method for solving Stokes interface problems. The method is constructed on local anisotropic mixed meshes, which are generated by fitting the interface through simple connection of intersection…

Numerical Analysis · Mathematics 2025-07-04 Geng Chenchen , Hua Wang , Fengren Zou

In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of $C^0$ vertex continuity of stresses introduced recently by…

Numerical Analysis · Mathematics 2020-03-19 Fleurianne Bertrand , Daniele Boffi , Rui Ma

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

Numerical Analysis · Mathematics 2021-05-05 Xiu Ye , Shangyou Zhang

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…

Numerical Analysis · Mathematics 2022-09-26 Franco Dassi , Alessio Fumagalli , Ilario Mazzieri , Giuseppe Vacca

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…

Numerical Analysis · Mathematics 2026-05-21 Pablo Brubeck , Charles Parker , Umberto Zerbinati

For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…

Numerical Analysis · Mathematics 2011-01-07 Shaohong Du , Xiaoping Xie

We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.

Numerical Analysis · Mathematics 2017-11-16 Tom Gustafsson , Rolf Stenberg , Juha Videman

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

The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…

Numerical Analysis · Mathematics 2023-01-18 Wietse M. Boon , Dennis Gläser , Rainer Helmig , Ivan Yotov