相关论文: Interior Penalty Mixed Finite Element Methods of A…

In general $n$-dimensional simplicial meshes, we propose a family of interior penalty nonconforming finite element methods for $2m$-th order partial differential equations, where $m \geq 0$ and $n \geq 1$. For this family of nonconforming…

New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…

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…

A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress…

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…

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…

The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between…

In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical…

In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal,…

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…

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…

We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…

We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…

Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…