Related papers: Error analysis for a viscoelastic phase separation…
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 numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the…
We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic…
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…
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…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…
We consider the numerical approximation of linear damped wave systems by Galerkin approximations in space and appropriate time-stepping schemes. Based on a dissipation estimate for a modified energy, we prove exponential decay of the…
We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed…
We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…