Related papers: CutVEM: Conforming virtual element method on embed…
In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning…
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains…
The EMI (Extracellular-Membrane-Intracellular) model describes electrical activity in excitable tissue, where the extracellular and intracellular spaces and cellular membrane are explicitly represented. The model couples a system of partial…
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
Generalized or extended finite element methods (GFEM/XFEM) are in general badly conditioned and have numerous additional degrees of freedom (DOF) compared with the FEM because of introduction of enriched functions. In this paper, we develop…
We consider convection-diffusion problems in time-dependent domains and present a space-time finite element method based on quadrature in time which is simple to implement and avoids remeshing procedures as the domain is moving. The…
In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
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…
In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…
The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…