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  • 1
    Electronic Resource
    Electronic Resource
    Heat Storage in Aquifers Analyzed by the Finite Element Method (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Ground water 20 (1982), S. 0 
    Details
    ISSN: 1745-6584
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Notes: In the design of ground-water heat pump systems the quantitative analysis of heat transport and heat storage is of great interest. A unified finite element approach to the transient nonlinear heat transport and heat storage problem is presented. The theory presented includes nonlinear physical properties and boundary conditions, coupled conductive and convective heat flow, freezing (phase change), and time-dependent heat input and output. The given theory is applied to two problems. The first problem is a transient study during a few years of heat storage in saturated clay. A pure conductive theory is used due to the small amount of convective water flow in clay. The second problem deals with transient heat transport in an aquifer according to coupled conduction-convection theory on a one-dimensional model problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1745-6584.1982.tb02747.x
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  • 2
    Electronic Resource
    Electronic Resource
    Interface-capturing finite element technique for transient two-phase flow (2003)
    Bradford : Emerald
    Engineering computations 20 (2003), S. 725-740 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: A numerical model is presented for the computation of unsteady two-fluid interfaces in nonlinear porous media flow. The nonlinear Forchheimer equation is included in the Navier-Stokes equations for porous media flow. The model is based on capturing the interface on a fixed mesh domain. The zero level set of a pseudo-concentration function, which defines the interface between the two fluids, is governed by a time-dependent advection equation. The time-dependent Navier-Stokes equations and the advection equation are spatially discretized by the finite element (FE) method. The fully coupled implicit time integration scheme and the explicit forward Eulerian scheme are implemented for the advancement in time. The trapezoidal rule is applied to the fully implicit scheme, while the operator-splitting algorithm is used for the velocity-pressure segregation in the explicit scheme. The spatial and time discretizations are stabilized using FE stabilization techniques. Numerical examples of unsteady flow of two-fluid interfaces in an earth dam are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400310488835
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  • 3
    Electronic Resource
    Electronic Resource
    Formulation and solution of hierarchical finite element equations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1213-1233 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general hierarchical formulation applicable to both elliptic and hyperbolic problems. Static and eigenvalue linear elastic problems as well as convection-diffusion problems are studied. The hierarchical formulation is well suited for adaptive procedures.For the convection-diffusion problem the hierarchical approximation is made in time only. Different hierarchical functions are proposed for different types of problems. Both weighted residual and least-squares formulations are applied. A combination of these two gives a penalty method with a constraint equation corresponding to the least-squares method. A whole class of time integration formulae is obtained. These are all suitable for adaptive procedures owing to the hierarchical approximation in the time domain. If a linear discontinuous hierarchical base function is used in the Galerkin weak formulation, the method so obtained corresponds to the discontinuous Galerkin method in time and is especially suited for convection dominated problems. The streamline-diffusion method is found to be the aforementioned penalty method.This paper also examines the sequence of nested equation systems that results from a hierarchical finite element formulation. Properties of these systems arising from static problems are investigated. The paper presents some new possibilities for iterative solution of hierarchic element equations, and different procedures are compared in a numerical example. Finally, a simple ID convection-diffusion problem clearly shows that the proposed hierarchical formulation in time gives a stable and accurate solution even for convection dominated flow.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260514
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  • 4
    Electronic Resource
    Electronic Resource
    Patch recovery based on superconvergent derivatives and equilibrium (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2703-2724 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a postprocessing technique is developed for determining first-order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points. It is an extension of the superconvergent patch recovery technique presented by Zienkiewicz and Zhu. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. The equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361603
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  • 5
    Electronic Resource
    Electronic Resource
    Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3417-3440 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Patch recovery based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the Superconvergent Patch Recovery (SPR), is studied for linear elasticity problems. The paper also presents a further improvement for recovery of derivatives near boundaries, SPREB, where either tractions or displacements are prescribed. This is made by inclusion of weighted residual errors at boundary points in the patch recovery. A pronounced improvement in the post processed gradients of the finite element solution is observed by this method.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372003
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  • 6
    Electronic Resource
    Electronic Resource
    Linked interpolation for Reissner-Mindlin plate elements: Part I - A simple quadrilateral (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3043-3056 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In most plate elements using the Reissner-Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables.Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed).In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361802
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  • 7
    Electronic Resource
    Electronic Resource
    On understanding and teaching of the finite element method (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 105-115 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; conceptual diagrams ; error estimation ; postprocessing ; teaching ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behaviour of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110204
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  • 8
    Electronic Resource
    Electronic Resource
    Matrix structural analysis with mixed variables (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 167-194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Use of mixed force and displacement variables may be the key to a reliable solution of many physical problems. For the analysis of elastic structures with large rigid motion the displacement method may fail due to illconditioning, but use of mixed variables (diacoptics) may work due to the possibility of using relative displacements within substructures. Analysis with mixed variables complicates the topology (the number of nodes and the number of variables at the nodes may vary in the same problem) so a careful study of the system analysis is required. Some general computer routines are given for handling topology, merging and solution of the sparse system equation. The solution routine handles constraints in a rational way and can also be used for decomposition of the system equation or for releasing inner nodes in superelements.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080113
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  • 9
    Electronic Resource
    Electronic Resource
    Adaptive and hierarchical weighted residual and least-squares time integration of convection-diffusion problems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 499-507 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In order to obtain an adaptive procedure for integration in time for convection-diffusion problems we make the integration by use of hierarchical approximation of the variation in time. Different hierarchical functions can be used for different types of problem. Both weighted residual and least-squares formulations are applied. A combination of those two gives a penalty method with a constraint equation corresponding to the least-squares method. A whole class of different methods is obtained, suitable for an adaptive procedure due to the hierarchical approximation in time. A combination of Galerkin in space and least-squares in time gives a number of higher order schemes in time. Some special cases of the general procedures can be identified. If a linear discontinuous hierarchical basis function is used in the Petrov-Galerkin weak formulation, the method obtained corresponds to the discontinuous Petrov-Galerkin method in time useful for convection-dominated problems. The streamline-diffusion method is found as the penalty method mentioned.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630040406
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