An efficient modification by Douglas and Kim of the usual alternating directions method reduces the splitting error from O(k2) to O(k3) in time step k. We prove convergence of this modified alternating directions procedure, for the usual non-mixed Galerkin finite element and finite difference cases, under the restriction that k/h2 is sufficiently small, where h is the grid spacing. This improve...

In this paper we show that mixed finite element methods for a fairly general second-order elliptic problem with variable coefficients can be given a nonmixed formulation. (Lower-order terms are treated, so our results apply also to parabolic equations.) We define an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection fini...

We devise a finite element methodology to trace quasi-static through-thickness crack paths in nonlinear elastic solids. The main feature of the proposed method is that it can be directly implemented into existing large scale finite element solvers with minimal effort. The mesh topology modifications that are essential in propagating a crack through the finite element mesh are accomplished by ut...

In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...

Abstract. The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We use standard mixed finite element method to approximate the elliptic electrostatic potentia...

A numerical analysis of the limit state for solids, with an adequately described structural geometry, is often a computationally demanding task, and there need effective method. The existing solid elements Finite Element Limit Analysis (FELA) are either expensive or require stress cutoff yield surface triaxial states. This paper presents partially mixed lower bound tetrahedral constant element ...

Abstract: We consider the anisotropic uniaxial formulation of the perfectly matched layer model (UPML). We prove the decay of different energies for the UPML, under certain assumptions, to demonstrate the well-posedness of this formulation. We present and analyze a mixed finite element method for the time domain discretization of the UPML to simulate wave propagation in unbounded domains in two...

This paper presents a comparative study on locally mass-conservative numerical methods for Darcy’s flows. The classical mixed finite element method (MFEM) is compared with the newly developed discontinuous finite volume method (DFVM) with and without weak over-penalization (WOP). These numerical methods are tested on three representative problems in porous media flows. In particular, locality, ...