相关论文: Comparing Lagrange and Mixed finite element method…
In this article, we present Bembel, the C++ library featuring higher order isogeometric Galerkin boundary element methods for Laplace, Helmholtz, and Maxwell problems. Bembel is compatible with geometries from the Octave NURBS package and…
This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
We describe in this work the numerical treatment of the Filament Based Lamellipodium Model (FBLM). The model itself is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel…
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…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
We introduce the harmonic virtual element method (harmonic VEM), a modification of the virtual element method (VEM) for the approximation of the 2D Laplace equation using polygonal meshes. The main difference between the harmonic VEM and…
The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems…
This thesis presents the development of a novel finite element library in Rust based on the principles of Finite Element Exterior Calculus (FEEC). The library solves partial differential equations formulated using differential forms on…
In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent…
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace-Beltrami problem posed on an $n$-dimensional…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…