Related papers: Mixed finite elements for elasticity on quadrilate…
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
In recent years, a new class of mixed finite elements -- compatible-strain mixed finite elements (CSMFEs) -- has emerged that uses the differential complex of nonlinear elasticity. Their excellent performance in benchmark problems, such as…
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner…
It is known that the 3-node hybrid triangular element MiSP3 and 4-node hybrid quadrilateral element MiSP4 presented by Ayad, Dhatt and Batoz (Int. J. Numer. Meth. Engng 1998, 42: 1149-1179) for Reissner-Mindlin plates behave robustly in…
The following work compares two popular mixed finite elements used to model subsurface flow and transport in heterogeneous porous media; the lowest order Raviart-Thomas element and the variational multiscale stabilized element. Comparison…
For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this paper…
We compute displacement and stress due to a normal fault by means of two-dimensional plane-strain finite-element analysis. To do so, we apply a system of forces to the fault nodes and develop an iterative algorithm serving to determine the…
This paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen-Lo$\grave{e}$ve expansion to stochastic…
We aimed to use finite element method to simulate the unique behaviors of liquid crystal elastomer, such as semi-soft elasticity, stripe domain instabilities etc. We started from an energy functional with the 2D Bladon-Warner-Terentjev…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated…
We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite…
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…
Constitutive equations are derived for the time-dependent behavior of particle-reinforced elastomers at isothermal loading with finite strains. A rubbery polymer is modelled as a network of macromolecules bridged by junctions which can slip…
This paper introduces a new family of mixed finite elements for solving a mixed formulation of the biharmonic equations in two and three dimensions. The symmetric stress $\bm{\sigma}=-\nabla^{2}u$ is sought in the Sobolev space…
In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…