Related papers: A trace finite element method for a class of coupl…
We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and…
The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting…
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In such methods a surface mesh is formed by approximately…
We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion.…
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…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
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…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
This work presents a novel unfitted finite element framework to simulate coupled surface-bulk problems in time-dependent domains, focusing on fluid-fluid interactions in animal cells between the actomyosin cortex and the cytoplasm. The…
This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
ESFEM is a method introduced in order to solve a linear advection-diffusion equation on an evolving two-dimensional surface with finite elements by using a moving grid with nodes sitting on and evolving with the surface. The evolution of…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…