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  • Articles  (14)
  • Engineering  (14)
  • discontinuous Galerkin finite element method  (1)
  • 1
    Electronic Resource
    Electronic Resource
    A study of the efficiency of iterative methods for linear problems in structural mechanics (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 209-218 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The efficiency of iterative methods in linear structural mechanics is studied. The efficiency concerns the calculation time, the numerical accuracy and the core storage needed. We state that iterative methods are effective in connection with hierarchical improvement of a primary approximation. Three iterative methods are studied: the conjugate gradient method preconditioned by a modified incomplete factorization matrix, the same method preconditioned by a matrix obtained from natural factors on elemental level, and a Jacobi integration preconditioned by viscous relaxation split in an element-by-element way. We make comparisons with direct methods, Gaussian elimination and factorization by use of natural factors.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220115
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  • 2
    Electronic Resource
    Electronic Resource
    Least-squares schemes for time integration of thermal problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 159-175 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper proposes a generalized least-squares time finite element procedure for analysis of transient field problems. It leads to a very general four parameter and two time level family of schemes. The free parameters are optimized in terms of accuracy, stability and oscillatory behaviour of the computational algorithm. In the case of linear problems an unconditionally stable scheme of fourth-order accuracy is obtained. Special choices of the free parameters also give a number of well-known time-integration schemes, such as the Zienkiewicz-Lewis third-order algorithm, the Goodrich scheme and standard schemes such as the Crank-Nicolson and backward fully implicit schemes. The main disadvantage of the higher order algorithm is a large bandwidth of the system matrix owing to the matrix terms of the form KTK. This drawback is reduced for special choices of the parameters by forming a product formula. Somewhat more computation is required than for popular schemes such as the generalized midpoint rule, depending on the prescribed variables. Numerical comparisons are made between the proposed higher order schemes and standard schemes.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240112
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  • 3
    Electronic Resource
    Electronic Resource
    An adaptive procedure for eigenvalue problems using the hierarchical finite element method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 319-335 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive procedure for the solution of the generalized linear eigenvalue problem within the hierarchical finite element method is described. The problem of finding for a given discretization, an upper limit eigenvalue that is accurate within a prescribed tolerance is especially studied. An error estimator is presented and a recomputational scheme for improved solutions is proposed. A numerical example is included.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240205
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  • 4
    Electronic Resource
    Electronic Resource
    Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100406
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  • 5
    Electronic Resource
    Electronic Resource
    SUPERCONVERGENT PATCH RECOVERY IN PROBLEMS OF MIXED FORM (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 207-217 
    Details
    ISSN: 1069-8299
    Keywords: plates ; finite elements ; mixed method ; error estimation ; superconvergent patch recovery ; adaptivity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch recovery (SPR technique) has been shown to be an effective postprocessing procedure in which an improved solution is obtained based on the original finite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order differential equations. The differential equation is here written as two coupled differential equations of second order leading to a mixed finite element procedure based on approximations of the moment and displacement fields. Two elements of mixed type are handled, namely a triangular plate element with constant moment field and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 13 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Two-dimensional mesh generation, adaptive remeshing and refinement (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1501-1526 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE-calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
    Additional Material: 39 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290709
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  • 7
    Electronic Resource
    Electronic Resource
    An adaptive finite element procedure for 2D dynamic transient analysis using direct integration (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 34 (1992), S. 997-1014 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive h-version finite element procedure is presented for a 2D elastodynamic transient analysis using direct integration. The procedure modifies the spatial discretization, i.e. the mesh, in time so that the spatial discretization error can be controlled in each time instant. We analyse an a priori error estimate for the total energy which shows that an a posteriori error estimate developed by Zienkiewicz and Zhu for linear elastostatics can reasonably be extended to dynamic transient analysis. For the time integration, both explicit and implicit time integration schemes can be coupled with the procedure. However, the study in this paper is confined to the use of the Newmark scheme. Numerical examples are used to study the performance of the error estimate and to illustrate the adaptive procedure. Obtained numerical results indicate that: (i) the extension of the Zienkiewicz-Zhu estimate to dynamic transient analysis is useful; (ii) the presented adaptive procedure can, in an efficient way, provide a finite element solution with a user-controlled accuracy.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620340321
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  • 8
    Electronic Resource
    Electronic Resource
    A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 273-292 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090402
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  • 9
    Electronic Resource
    Electronic Resource
    The effectivity of the Zienkiewicz-Zhu error estimate and two 2D adaptive mesh generators (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 687-699 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple ‘averaging’ procedure; (2) these two mesh generators are basically comparable.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090808
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  • 10
    Electronic Resource
    Electronic Resource
    Improved element stresses for node and element patches using superconvergent patch recovery (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 619-627 
    Details
    ISSN: 1069-8299
    Keywords: post processing ; node patch ; element patch ; superconvergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods to calculate improved postprocessed stresses in elements for the superconvergent patch recovery technique are developed. Based on improved stresses on node patches, the improved element stresses are obtained by using weighting of patch solutions from different patch assembly points. An alternative method is to directly calculate the element stresses for an element patch based on weighted information. Numerical examples show that the performances of the two procedures are of about the same quality.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110708
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