相关论文: An interface-enriched generalized finite element f…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
In this article we study a mixed finite element formulation for solving the Stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor, on an interface that splits the domain into two subdomains.…
A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3,…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…
In this paper we study a moving free boundary problem related to the the cavitation modeling in lubricated devices. More precisely, a characteristics method combined with a weak formulation in a mixed form is introduced for the Elrod-Adams…
This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed,…
We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong…
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is…
A fluid-structure interaction technique for the simulation of inflatable structures is introduced. The presented finite-element/boundary-element (FEBE) technique couples an isogeometric finite element discretization of a flexible shell…
The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the…
In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature of our scheme is an adaptive two-mesh approach that, in addition to the standard enrichment of a conforming finite element discretization via…