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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 develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…

Numerical Analysis · Mathematics 2018-02-09 Tobin Isaac

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

For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…

Numerical Analysis · Mathematics 2016-03-04 Zhiqiang Cai , Cuiyu He , Shun Zhang

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…

Numerical Analysis · Mathematics 2026-03-03 Huangxin Chen , Yuxiang Chen , Jisheng Kou , Shuyu Sun

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

Numerical Analysis · Mathematics 2013-08-05 Erik Burman

The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…

Numerical Analysis · Computer Science 2009-09-30 G. Haikal

In this paper we consider a three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns. For parameter-robust stability analysis, we first show a priori estimates of the…

Numerical Analysis · Mathematics 2018-07-02 Jeonghun J. Lee

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…

Numerical Analysis · Mathematics 2023-01-13 Sebastian Schwarzacher , Bangwei She , Karel Tuma

In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…

Numerical Analysis · Mathematics 2024-01-01 Johannes Kraus , Kundan Kumar , Maria Lymbery , Florin Adrian Radu

We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…

Numerical Analysis · Mathematics 2017-10-06 Pavel Bochev , James Cheung , Max Gunzburger , Mauro Perego

A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…

Numerical Analysis · Mathematics 2020-07-31 Balázs Kovács , Buyang Li , Christian Lubich

A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…

Numerical Analysis · Mathematics 2021-12-21 Sajje Lee Calfy , John A. Evans , David Kamensky

We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger-Reissner…

Numerical Analysis · Mathematics 2017-03-24 Trygve Baerland , Jeonghun J. Lee , Kent-Andre Mardal , Ragnar Winther

The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…

Numerical Analysis · Mathematics 2009-03-25 Xiaobing Feng , Yinnian He

The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…

Numerical Analysis · Mathematics 2017-09-21 Florian Zwicke , Sebastian Eusterholz , Stefanie Elgeti

Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic composites. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip…

Analysis of PDEs · Mathematics 2022-06-17 Miao-jung Yvonne Ou , Silvia Jiménez Bolaños

This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…

Numerical Analysis · Mathematics 2021-04-07 Eric Neiva , Santiago Badia

In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…

Numerical Analysis · Mathematics 2025-10-15 Xindan Zhang , Jianping Zhao , Yanren Hou

We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the…

Numerical Analysis · Mathematics 2019-04-01 Qingguo Hong , Johannes Kraus , Maria Lymbery , Mary Fanett Wheeler