Showing papers on "Smoothed finite element method published in 1989"
TL;DR: A portable, power operated, hand cultivator comprising a frame having a motor supported thereon which oscillates two or more generally vertically disposed cultivator tines extending downwardly from the frame.
408 citations
TL;DR: In this paper, five different techniques for a posteriori error estimation of adaptive finite element methods for linear elliptic boundary value problems are presented, referred to as the residual estimation method, the duality method, subdomain residual method, a method based on interpolation theory, and a post-processing method.
365 citations
234 citations
89 citations
TL;DR: In this article, the first in the series addressing the h-p version of the finite element method for parabolic equations is presented, where the p-version with one single time element is used.
Abstract: The paper is the first in the series addressing the h-p version of the finite element method for parabolic equations. The h-p version is applied to both time and space variables. The present paper addresses the case when in time the p-version with one single time element is used. Error estimation is given and numerical computations are presented.
77 citations
TL;DR: In this paper, the mixed finite element method was introduced as a viable numerical procedure for the boundary controllability of the linear wave equation, but due to the approximation problems of the normal derivative on the boundary, the method becomes unstable as the mesh is refined.
Abstract: : This paper introduces the mixed finite element method as a viable numerical procedure for the boundary controllability of the linear wave equation. Another numerical implementation using Galerkin finite elements has been investigated. However, due to approximation problems of the normal derivative on the boundary, the method becomes unstable as the mesh is refined. To correct for the ill-posedness of the approximate problem, a Tychonoff regularization method was implemented. The aforementioned paper also presents other possible remedies; among them is the mixed finite element method. The fixed finite element approximation is a plausible procedure to overcome these difficulties since the derivative at certain nodal values arises naturally from the formulation.
68 citations
TL;DR: In this paper, a decoupled finite element streamline-upwinding scheme was developed for viscoelastic flows, where the streamline integration of the constitutive equation was replaced by a Galerkin discretization with streamline upwinding applied to the convective terms.
Abstract: Parallel to a recently reported mixed finite element method by Marchal and Crochet, a new decoupled finite element streamline-upwinding scheme is developed for viscoelastic flows. While relatively cheap Picard iteration used previously in our streamline element method is maintained, the streamline integration of the constitutive equation is replaced by a Galerkin discretization with streamline-upwinding applied to the convective terms. Using a Maxwell or an Oldroyd-B model and a simple bilinear interpolation for the extra-stress without element subdivision, our calculation of the flow through a four-to-one circular contraction has reached a Weissenberg number limit slightly higher than that reached by the corresponding mixed method with a two by two element subdivision for the extra-stress. Numerical experiments also show that both the conventional Galerkin and the consistent streamline-upwind/Petrov-Galerkin methods give poorer performance than the non-consistent streamline-upwinding approach, confirming results found by the mixed method. The validity of the non-consistent upwinding approach is discussed, and we show that it leads to effectively changed constitutive models which yield smoothed solutions and increased stability.
60 citations
TL;DR: In this article, the authors employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses.
Abstract: This paper presents some mixed formulations for finite element analysis of magnetostatic and electrostatic problems We employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and the scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses We also give brief comments on the use of the vector potential for the magnetostatic problem
59 citations
TL;DR: In this article, a comprehensive groundwater solute transport simulator is developed based on the modified method of characteristics (MMOC) combined with the Galerkin finite element method for the transport equation and the mixed finite element (MFE) method for groundwater flow equation.
Abstract: A comprehensive groundwater solute transport simulator is developed based on the modified method of characteristics (MMOC) combined with the Galerkin finite element method for the transport equation and the mixed finite element (MFE) method for the groundwater flow equation. The preconditioned conjugate gradient algorithm is used to solve the two large sparse algebraic system of equations arising from the MMOC and MFE discretizations. The MMOC takes time steps in the direction of flow, along the characteristics of the velocity field of the total fluid. The physical diffusion and dispersion terms are treated by a standard finite element scheme. The crucial aspect of the MMOC technique is that it looks backward in time, along an approximate flow path, instead of forward in time as in many method of characteristics or moving mesh techniques. The MFE procedure involves solving for both the hydraulic head and the specific discharge simultaneously. One order of convergence is gained by the MFE method, as compared with other standard finite element methods, and therefore more accurate velocity fields are simulated. The overall advantages of the MMOC-MFE method include minimum numerical oscillation or grid orientation problems under steep concentration gradient simulations, and material balance errors are greatly reduced due to a very accurate velocity simulation by the MFE method. In addition, much larger time steps with Courant number well in excess of 1, as compared with the standard Galerkin finite element method, can be taken on a fixed spatial grid system without significant loss of accuracy.
54 citations
TL;DR: In this article, the authors generalized the finite element method for localization analysis to account for finite deformations and for material rate dependence, and demonstrated the performance of the enhanced element in a problem involving shear localization in a plane strain tensile bar.
Abstract: The finite element method for localization analysis of Ortiz et al. [Comp. Methods Appl. Mech. Engrg. 61] is generalized to account for finite deformations and for material rate dependence. Special shape functions are added to the finite element basis to reproduce band-like localized deformation modes. The amplitudes of these additional modes are eliminated locally by static condensation. The performance of the enhanced element is illustrated in a problem involving shear localization in a plane strain tensile bar. Solutions based on the enhanced element are compared with corresponding results obtained from the underlying compatible isoparametric quadrilateral element and from crossedtriangular and uniformly reduced integration elements. In the finite deformation context, the enhanced element solution is not very sensitive to the precise specification of initial orientation of the additional band-like modes. The enhanced element formulation described here can be used for a broad range of rate independent and rate dependent material behaviors in two dimensional and three dimensional problems.
TL;DR: In this article, a variationally based coupling for the finite element and boundary element methods was developed by combining the variational forms for the boundary element and finite element subdomains to obtain a global variational form and then choosing a suitable set of test and trial functions.
TL;DR: In this paper, error estimates for some spatially discrete Galerkin finite element methods for a non-linear heat equation are shown for the enthalpy as a new dependent variable, and also for the application of the Kirchhoff transformation and interpolation of the nonlinear coefficients into standard Lagrangian finite element spaces.
Abstract: Error estimates are shown for some spatially discrete Galerkin finite element methods for a non-linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non-linear coefficients into standard Lagrangian finite element spaces.
28 Mar 1989
TL;DR: In this paper, a three-dimensional finite element method using the A-phi formulation for analyzing time-periodic nonlinear magnetic fields with eddy currents has been developed.
Abstract: A three-dimensional finite element method using the A- phi formulation for analyzing time-periodic nonlinear magnetic fields with eddy currents has been developed. The CPU time of this method can be reduced to below that of the conventional step-by-step method, because the new method calculates the time-periodic phenomena directly, not through the transient phenomena. The finite element discretization of the method is described in detail. As an example of application, a loaded transformer is analyzed. >
TL;DR: In this paper, the effect of interface friction between two bodies in contact is modeled by a regularized Coulomb's law, based on which both the displacements and contact pressure in an element were independently approximated.
01 Jan 1989
TL;DR: This paper introduces an alternative mathematical treatment based on a direct minimisation of the underlying energy integral using the Finite Element Method, and its principal advantages for modelbased image interpretation are explained.
Abstract: Deformable models of elastic structures have been proposed for use in image analysis. Previous work has used a variational approach, based on the EulerLagrange theory. In this paper an alternative mathematical treatment is introduced, based on a direct minimisation of the underlying energy integral using the Finite Element Method. The method is outlined and demonstrated, and its principal advantages for modelbased image interpretation are explained.
TL;DR: It is shown that the optimal asymptotic convergence rate is achieved, demonstrating the effectiveness of the intelligent multiple-level localh-refinement.
Abstract: This paper discusses an automatic, adaptive finite element modeling system consisting of mesh generation, finite element analysis, and error estimation. The individual components interact with one another and efficiently reduce the finite element error to within an acceptable value and perform only a minimum number of finite element analyses.
TL;DR: This work considers the effect of the choice of finite element basis on the conditioning and iterative solution of the algebraic systems obtained using high degree finite elements (p-methods).
Abstract: This work considers the effect of the choice of finite element basis on the conditioning and iterative solution of the algebraic systems obtained using high degree finite elements (p-methods). This issue is fundamental to the performance ofp-methods and to the increased use of iterative solution techniques both for standard finite element analysis and also in adaptivep solutions. The central ideas also apply to high degree spectral methods (global expansion methods).
TL;DR: In this paper, a new numerical simulation of two-phases incompressible fluid flow (2D and 3D) is devoted to a new simulation method, which is based on hybrid dual finite element method (FEM) with suppression of the grid effect.
Abstract: This paper is devoted to a new numerical simulation of two-phases incompressible fluid flow (2D and 3D). Velocity and pressure equations are solved by an hybrid dual finite element method (FEM) with suppression of the grid effect. A Van Leer upwind scheme is used for the saturation equation, in order to reduce the front dispersion. For equal computational cost this method is more accurate than the classical finite difference method (FDM) used in reservoir simulation.
TL;DR: The use of the method of constraints for enforcing the zero divergence condition in vectorial finite-element schemes is discussed and partial success in extending the method to multielement cases is reported.
Abstract: The use of the method of constraints for enforcing the zero divergence condition in vectorial finite-element schemes is discussed. An earlier implementation of the method was shown to produce the correct solution for a 3-D resonant cavity problem modeled by a single finite element. Partial success in extending the method to multielement cases is reported. The reduction in matrix size alone would justify the development of the technique for general multielement grids, but it will require the implementation of a global approach to the method of constraints. >
TL;DR: In this article, a linear partial differential equation of diffusion type was used for solving a pipeline and linear and cubic interpolating polynomials were used for the finite element method.
TL;DR: Recent, major improvements to finite element methodology are outlined and the implementation of a moving finite element technique, in which the mesh nodes are allowed to move adaptively to achieve an accurate solution, is described.
TL;DR: In this article, a new Petrov-Galerkin formulation for axisymmetric shells with shear deformation is derived, and additional stability and accuracy are gained from thin to moderately thick shells, as shown in representative numerical tests.
Abstract: Consistently perturbing the Galerkin finite element discretization of the Hellinger-Reissner principle, a new Petrov-Galerkin formulation for axisymmetric shells with shear deformation is derived. Additional stability and accuracy are gained from thin to moderately thick shells, as shown in representative numerical tests. Some unstable Galerkin finite element interpolations are proved to be stable and convergent with the new approach.
01 Jan 1989
TL;DR: In this paper, a linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems, where the element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form.
Abstract: A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.
TL;DR: A distributed data structure that allows very efficient massively parallel computations on irregular two and three dimensional finite element meshes and an alternative approach to interprocessor communication that is based on an optimal mapping of the processors onto the finite elements of the irregular mesh are proposed.
Abstract: This paper reports on our early experience with solving large scale finite element dynamic problems on the Connection Machine. We describe a distributed data structure that allows very efficient massively parallel computations on irregular two and three dimensional finite element meshes. The often encountered mesh irregularities inhibit the use of the NEWS communication package. We propose an alternative approach to interprocessor communication that is based on an optimal mapping of the processors onto the finite elements of the irregular mesh. Our parallel data structure and processor mapping are applied to finite element wave propagation problems on the CM-2.