Related papers: A surface finite element method for computational …
We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both…
The aim of this paper is to develop suitable models for the phenomenon of cell blebbing, which allow for computational predictions of mechanical effects including the crucial interaction of the cell membrane and the actin cortex. For this…
We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility.…
Surfactants play an important role in various physiological and biomechanical applications. An example is the respiratory system, where pulmonary surfactants facilitate the breathing and reduce the possibility of airway blocking by lowering…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic…
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…
This study develops a polygonal cell-based smoothed finite element method (CSFEM) for two-dimensional seepage analyses in porous media, covering steady-state, transient, and free-surface problems. Wachspress interpolation on convex…
This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop for our analysis are: (i) a new density result in $GSBV^{p}$ of functions satisfying a…
Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase…
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a…
We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Membrane computing is a well-established and successful research field which belongs to the more general area of molecular computing. Membrane computing aims at defining parallel and non-deterministic computing models, called membrane…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…