Related papers: A multipoint stress mixed finite element method fo…
In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special…
In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of $C^0$ vertex continuity of stresses introduced recently by…
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
In the context of global/goal-oriented error estimation applied to computational mechanics, the need to obtain reliable and guaranteed bounds on the discretization error has motivated the use of residual error estimators. These estimators…
A block diagonal preconditioner with the minimal residual method and a block triangular preconditioner with the generalized minimal residual method are developed for Hu-Zhang mixed finite element methods of linear elasticity. They are based…
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…
Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element…
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
Two novel version of weak form quadrature elements are proposed based on Lagrange and Hermite interpolations, respectively, for a sec- ond strain gradient Euler-Bernoulli beam theory. The second strain gradient theory is governed by eighth…
We present a theoretical method for deriving the stress tensor and elastic response of ordered systems within a Ginzburg-Landau type density field theory in the linear regime. This is based on spatially coarse graining the microscopic…
We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces in multi-ply multi-directional composite laminates. In…
This article develops a weak Galerkin least-squares (WG--LS) finite element method for first-order linear convection equations in non-divergence form. The method is formulated using discontinuous finite element functions and does not…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
We develop a numerical scheme for a two-phase immiscible flow in heterogeneous porous media using a structured grid finite element method, which have been successfully used for the computation of various physical applications involving…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories…
In this paper, a MATLAB package bdm_mfem for a linear Brezzi-Douglas- Marini (BDM) mixed finite element method is provided for the numerical solution of elliptic diffusion problems with mixed boundary conditions on unstructured grids. BDM…