Related papers: Stable Mixed Finite Elements for Linear Elasticity…
This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
Contact involving soft materials often combines dry adhesion, sliding friction, and large deformations. At the local level, these three aspects are rarely captured simultaneously, but included in the theoretical models by Mergel et al.…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…
A new family of mixed finite element methods$-$compatible-strain mixed finite element methods (CSFEMs)$-$are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
Stiffness degradation and progressive failure of composite laminates are complex processes involving evolution and multi-mode interactions among fiber fractures, intra-ply matrix cracks and inter-ply delaminations. This paper presents a…
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be…
We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…
In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…