Related papers: Parameter-Robust Preconditioners for A Four-Field …
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially…
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…
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of…
We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block…
This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
Numerical modeling of proton exchange membrane fuel cells is at the verge of becoming predictive. A crucial requisite for this, though, is that material properties of the membrane-electrode assembly and their functional dependence on the…
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…
This paper introduces a new nonlinear topology optimization framework which employs porohyperelasticity for providing computational design of pneumatic soft actuators. Density-based topology optimization is used with the objective of…
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…
This paper presents a mixed finite element framework for coupled hydro-mechanical-chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin…
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…
Understanding the coupled thermo-mechanical behaviour of compacted granular beds can benefit various industrial applications, such as pebble bed design in fusion reactors. In this study, a thermo-mechanical discrete element method based on…
In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish…
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…
We investigate the multi-order parameter phase field model of Steinbach and Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385-393] concerning its…
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix-fracture interfaces, as well as…