Virtual element methods for the three-field formulation of time-dependent linear poroelasticity

Stabilized Lowest-Order Finite Element Approximation for Linear Three-Field Poroelasticity

A stabilized conforming finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is presented. We use the lowest possible approximation order: piecewise constant approximation for the pressure, and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservatio...

Locking-Free Finite Element Methods for Poroelasticity

We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as Biot’s consolidation problem. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and both continuous and discrete formulations are analyzed as ...

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the nu...

Linear Poroelasticity

Delay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...