Related papers: Analysis of an abstract mixed formulation for visc…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the…
The aim of the present work is to derive a error estimates for the Laplace eigenvalue problem in mixed form, by means of a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is…
In this work, we present a novel approach to the mathematical analysis of equations with memory based on the notion of a state, namely, the initial configuration of the system which can be unambiguously determined by the knowledge of the…
In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
This paper presents an analytical model of punctual elastic contact between a rigid body of arbitrary geometry and a plane surface. A simple analytical model is developed in order to evaluate the contact force knowing the volume of…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…
The spinning of slender viscous jets can be described asymptotically by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas the well-established string models possess only solutions for…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We outline a 2D algorithm for solving incompressible flow--structure interaction problems for mixed rigid/soft body representations, within a consistent framework based on the remeshed vortex method. We adopt the one--continuum formulation…
We present an a posteriori error analysis for the mixed virtual element method (mixed VEM) applied to second order elliptic equations in divergence form with mixed boundary conditions. The resulting error estimator is of residual-type. It…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
We analyse a coupled 3D-2D model with a free fluid governed by Stokes flow in the bulk and a poroelastic plate described by the Biot-Kirchhoff equations on the surface. Assuming the form of a double perturbed saddle-point problem, the…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the…