Showing papers on "Smoothed finite element method published in 1983"
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01 Jan 1983846 citations
TL;DR: Statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models as mentioned in this paper, and the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy.
Abstract: Statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models The error on constitutive law for these fields yields an expression of the finite element error Moreover, the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy
670 citations
TL;DR: The notion of a generalized finite element method is introduced and this class of methods is analyzed and their relation to mixed methods is discussed.
Abstract: The notion of a generalized finite element method is introduced. This class of methods is analyzed and their relation to mixed methods is discussed. The class of generalized finite element methods offers a wide variety of computational procedures from which particular procedures can be selected for particular problems. A particular generalized finite element method which is very effective for problems with rough coefficients is discussed in detail.
426 citations
395 citations
TL;DR: Application of the mesh generator to a variety of problems in magnetic field design shows it to be one of the most powerful and easy to use systems yet devised.
Abstract: A two-dimensional finite element analysis package is described which automatically generates optimal finite element meshes for magnetic field problems. The system combines the concept of Delaunay triangulation with variational principles to provide a grid which adapts to the characteristics of the solution. In this procedure, two different approximate solutions to the magnetic field are derived, the difference between the two approximate solutions providing an element by element measure of the accuracy of the solution. By refining those elements having the largest errors and recomputing the solution iteractively, finite element meshes having a uniforrn error density are obtained. The system is menu oriented and utilizes multiple command and display windows to create and edit the object description interactively. Matrix solution is by means of a rapid pre-conditioned conjugate gradient algorithm, and a wide variety of post-processing operations are supported. Application of the mesh generator to a variety of problems in magnetic field design shows it to be one of the most powerful and easy to use systems yet devised.
153 citations
TL;DR: In this paper, a finite dimensional stability test for checking velocity/pressure finite element trial spaces is presented and applications are made to a new class of element pairs proposed in this paper as well as to existing spaces.
Abstract: A finite dimensional stability test for checking velocity/pressure finite element trial spaces is presented. Applications are made to a new class of element pairs proposed in this paper as well as to existing spaces.
145 citations
TL;DR: A computationally useful criterion for grid optimization is derived, based on a measure of the interpolation error associated with the finite element model, intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom.
138 citations
TL;DR: In this paper, a general finite element model is proposed to analyze transient phenomena in thermoelastic solids and time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis.
Abstract: A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.
115 citations
TL;DR: In this paper, the behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.
Abstract: Second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered. The behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.
TL;DR: In this article, the minimum truncation error of one and two-dimensional Burgers' equations with moderate to severe internal and boundary gradients was compared with three, five-, and seven-point finite difference schemes with linear, quadratic, and cubic rectangular finite element schemes.
TL;DR: In this paper, a new formulation of finite element method is accomplished by the Hellinger-Reissner principle for which the stress equilibrium conditions are not introduced initially but are brought in through the use of additional internal displacement parameters.
TL;DR: In this paper, the implementation of a combined boundary element-finite element analysis capability is discussed and a comparison is made between the finite element, boundary element and coupled method as applied to unbounded problems in elasticity and plasticity.
Abstract: The implementation of a combined boundary element-finite element analysis capability is discussed. A comparison is then made between the finite element, boundary element and coupled method as applied to unbounded problems in elasticity and plasticity.
TL;DR: In this article, the use of numerical methods in simulating and solving problems that arise in the electroheat industry is reviewed. But the focus is on the coupled electrothermal and induction stirring problems that are typical of this industry.
Abstract: This paper reviews the use of numerical methods in simulating and solving problems that arise in the electroheat industry. Particular attention is given to the coupled electrothermal and induction stirring problems that are typical of this industry. Following a brief review of the nature of electrothermal problems, the Finite Difference, Volume Integral Equation and Finite Element simulation techniques are critically examined. It is shown that each technique has a definite role and each is illustrated with practical examples. A brief discussion of unsolved problems is presented.
TL;DR: In this paper, a mixed finite element method based on rectangular elements was proposed for solving the two-dimensional elasticity equations, and error estimates for a method proposed by Taylor and Zienkiewicz and for some new variants of the known equilibrium methods were proved.
Abstract: We analyze some mixed finite element methods, based on rectangular elements, for solving the two-dimensional elasticity equations. We prove error estimates for a method proposed by Taylor and Zienkiewicz and for some new variants of the known equilibrium methods. A numerical example is given demonstrating the performance of the various algorithms considered. 1. Introduction. In the numerical solution of problems of continuum mechanics, the stresses are normally of primary interest in the elastic region. It is therefore natural to design the numerical algorithms so that the stresses can be obtained directly without first computing the displacements. Such methods can be derived from the dual variational formulation of the elasticity problem. The corresponding finite element algorithms are usually formulated as mixed methods where both the displacements and the stresses are first approximated, and the displacements are then eliminated from the discrete equations. In many cases the elimination can be rather effectively done using penalty/perturbation techniques or their iterative variants; cf. (3), (11), (12). The best known finite element methods of the above type are the so-called equilibrium methods, first proposed by Fraejis de Veubeke (17) (cf. also (14), (16), (18)) and analyzed theoretically by Johnson and Mercier (9) (cf. also (8)). In these methods, one uses specific composite elements which allow the equilibrium condi- tion between the stresses and the volume load to be satisfied exactly in the case where the volume load is zero.
TL;DR: In this paper, two finite element algorithms suitable for long-term simulation of geothermal reservoirs are presented, which use a diagonal mass matrix and a Newton iteration scheme, and are shown to be competitive with existing methods.
Abstract: Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.
TL;DR: In this article, the MAXWELL's equations are used to solve the non-linear electromagnetic problem in axisymmetric induction heating devices, and the numerical methods are described, and in order to reduce the computation time, improvements are proposed.
Abstract: AXSYM package described in this paper is a step by step finite element method which solves the non-linear electromagnetic problem in axisymmetric induction heating devices. From the MAXWELL's equations, some standard assumptions lead to a 2D-scalar problem ; then the numerical methods are described, and in order to reduce the computation time, some improvements are proposed. The paper concludes with a comparison between experimental and numerical results.
01 Jan 1983
TL;DR: The use of mixed methods in a two-dimensional finite difference compositional simulator to reduce problems caused by numerical dispersion is presented.
Abstract: Previous studies have shown that standard finite difference techniques cause numerical dispersion and grid orientation problems when used to simulate enhanced recovery processes with adverse mobility ratios. In compositional simulation, numerical dispersion can diffuse sharp fluid interfaces yielding erroneous predictions of fluid compositions and corresponding errors in the velocities of the miscible frontal advance. Numerical dispersion can also effect the computed locations of the boundaries of the regions of single-phase and two-phase flow. Inaccurate fluid velocities and suboptimal use of upstream weighting of transport terms combine to cause many aspects of the numerical dispersion and grid orientation problems. A mixed finite element method has been developed to obtain more accurate approximations to the fluid velocities. In this method the Darcy velocities are considered as primary variables together with the total fluid pressure. Although finite element techniques are used to compute the more accurate fluid velocities, these velocities are then incorporated into a more standard finite difference method for the bulk of the simulation process. This paper presents the use of mixed methods in a two-dimensional finite difference compositional simulator to reduce problems caused by numerical dispersion. Comparisons are made with a standard finite difference simulator on problems involving immiscible displacementmore » and multiple contact miscibility phenomena.« less
TL;DR: The experimental results show that this two-step scheme is more efficient than the reverse Cuthill-McKee algorithm applied directly to the nodes, in terms of both execution time and the number of fill-in entries, particularly when higher order finite elements are used.
Abstract: : A two-step approach to finite element ordering is introduced. The scheme involves ordering of the finite elements first, based on their adjacency, followed by a local numbering of the nodal variables. The ordering of the elements is performed by the Cuthill-Mckee algorithm. This approach takes into consideration the underlying structure of the finite element mesh, and may be regarded as a natural finite element ordering scheme. The experimental results show that this two-step scheme is more efficient than the reverse Cuthill-McKee algorithm applied directly to the nodes, in terms of both execution time and the number of fill-in entries, particularly when higher order finite elements are used. In addition to its efficiency, the two-step approach increases modularity and flexibility in finite element programs, and possesses potential application to a number of finite element solution methods. (Author)
TL;DR: Adaptive finite element technology has the potential for reducing the cost of structural analysis significantly as mentioned in this paper, and two different approaches to improve upon the solution accuracy: (1) selective mesh refinement with low order elements (the h-version of the finite element method); and (2) through the addition of progressively higher order hierarchic shape functions (the p-version) are the most promising approach.
Abstract: Adaptive finite element technology has the potential for reducing the cost of structural analysis significantly. There are two different approaches to improve upon the solution accuracy: (1) By selective mesh refinement with low order elements (the h-version of the finite element method); and (2) through the addition of progressively higher order hierarchic shape functions (the p-version of the finite element method). Adaptivity based on the p-version is the most promising approach because the p-version offers greater efficiency than the h-version. Full utilization of the adaptive process in stress analysis requires that local a posteriori error estimates be developed in norms other than energy norms. One possibility in the use of a root-mean-square measure of stress, provided the error can be estimated without the need to know the exact solution.
01 Jan 1983
TL;DR: In this paper, Lanczos algorithm is used to solve nonlinear algebraic, discrete equations arising from the application of the finite element method to initial-boundary value problems in structural mechanics.
TL;DR: In this paper, a hybrid finite element scheme, based on assumed deviatoric fluid stresses in the element and continuous velocity fields at the element-boundaries, is presented, subject a priori to the constraints of balance of momenta, and its versatility is demonstrated through a few numerical examples.
TL;DR: In this article, a hybrid finite element method based on an assumed stress field is presented, where the unknowns in the final system of finite element equations are the nodal velocities, and the constant term in the arbitrary pressure field over each element.
01 Jan 1983
TL;DR: In this article, the location of nodes of the finite element grid is optimized by reducing the error associated with interpolation of the exact solution, using functions from finite element space, while keeping the number of degrees of freedom fixed.
Abstract: Finite element solutions of improved quality are obtained by optimizing the location of nodes of the finite element grid, while keeping the number of degrees of freedom fixed. The formulation of the grid optimization problem is based on the reduction of error associated with interpolation of the exact solution, using functions from the finite element space. Element sizes are selected as design variables: length in R1 and area in R2. Analytically derived optimality conditions are presented and an approximation to these conditions is introduced to obtain a set of operationally useful equations that can be used as guidelines for construction of improved grids. Example problems are given for illustration.