English
Related papers

Related papers: Fully-Mixed Virtual Element Method for the Biot Pr…

200 papers

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

Numerical Analysis · Mathematics 2026-01-21 Amy de Castro , Hyesuk Lee

In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are…

Numerical Analysis · Mathematics 2024-12-18 Stefano Berrone , Stefano Scialò , Gioana Teora

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

Numerical Analysis · Mathematics 2024-12-20 Jay Gopalakrishnan , Philip L. Lederer , Joachim Schöberl

We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…

Numerical Analysis · Mathematics 2018-02-12 Markus Bause

We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…

Analysis of PDEs · Mathematics 2025-08-26 Jeffrey Kuan , Sunčica Čanić , Boris Muha

The objective of this study is to highlight the effect of porosity variation in a topology optimization process in the field of fluid dynamics. Usually a penalization term added to momentum equation provides to get material distribution.…

Fluid Dynamics · Physics 2020-04-23 Rakotobe Michaël , Ramalingom Delphine , Cocquet Pierre-Henri , Bastide Alain

This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…

Numerical Analysis · Mathematics 2025-12-25 Liet Vo

We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear…

Numerical Analysis · Mathematics 2019-02-05 Ilona Ambartsumyan , Vincent J. Ervin , Truong Nguyen , Ivan Yotov

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…

Numerical Analysis · Mathematics 2022-11-30 Thomas Frachon , Sara Zahedi

We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation of the dynamic permeability in the frequency domain to…

Analysis of PDEs · Mathematics 2024-06-04 Jakob S. Stokke , Markus Bause , Nils Margenberg , Florin A. Radu

In this work, we introduce a novel algorithm for the Biot problem based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discretization of the flow. The method has several assets, including,…

Numerical Analysis · Mathematics 2016-02-25 Daniele Boffi , Michele Botti , Daniele A. Di Pietro

In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…

Numerical Analysis · Mathematics 2024-01-18 Patrick Bammer , Lothar Banz , Andreas Schröder

In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…

Numerical Analysis · Mathematics 2016-11-29 P. F. Antonietti , G. Manzini , M. Verani

A micro-hydromechanical model for granular materials is presented. It combines the discrete element method (DEM) for the modeling of the solid phase and a pore-scale finite volume (PFV) formulation for the flow of an incompressible pore…

Soft Condensed Matter · Physics 2013-12-17 Emanuele Catalano , Bruno Chareyre , Eric Barthélémy

In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…

Numerical Analysis · Mathematics 2024-06-13 David Mora , Jesus Vellojin , Nitesh Verma

In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems…

Numerical Analysis · Mathematics 2024-04-01 Si Xiao , Xianmin Xu

We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…

Numerical Analysis · Mathematics 2018-11-13 Douglas N. Arnold , Jeonghun J. Lee

We consider a recent plate model obtained as a scaled limit of the three dimensional Biot system of poro-elasticity. The result is a "2.5" dimensional linear system that couples traditional Euler-Bernoulli plate dynamics to a pressure…

Analysis of PDEs · Mathematics 2021-05-27 Elena Gurvich , Justin T. Webster

In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva