Related papers: A surface finite element method for computational …
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching energy. We discuss properties of this energy functional such as…
The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
The aim of this paper is to provide a mathematical model for spatial distribution of membrane electrical potential changes by fluorescence diffuse optical tomography. We derive the resolving power of the imaging method in the presence of…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour is particularly important for understanding the hygro-mechanical…
The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely…
From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the…