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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Calcolo 37 (2000), S. 65-77 
    ISSN: 1126-5434
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract: Adaptive mesh design based on a posteriori error control is studied for finite element discretisations for variational problems of Signorini type. The techniques to derive residual based error estimators developed, e.g., in ([2, 10, 20]) are extended to variational inequalities employing a suitable adaptation of the duality argument [17]. By use of this variational argument weighted a posteriori estimates for controlling arbitrary functionals of the error are derived here for model situations for contact problems. All arguments are based on Hilbert space methods and can be carried over to the more general situation of linear elasticity. Numerical examples demonstrate that this approach leads to effective strategies for designing economical meshes and to bounds for the error which are useful in practice.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 19 (1997), S. 434-446 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Recently a refined approach to error control in finite element (FE) discretisations has been proposed, Becker and Rannacher (1995b), (1996), which uses weighted a posteriori error estimates derived via duality arguments. The conventional strategies for mesh refinement in FE models of problems from elasticity theory are mostly based on a posteriori error estimates in the energy norm. Such estimates reflect the approximation properties of the finite element ansatz by local interpolation constants while the stability properties of the continuous model enter through a global coercivity constant. However, meshes generated on the basis of such global error estimates are not appropriate in cases where the domain consists of very heterogeneous materials and for the computation of local quantities, e.g., point values or contour integrals. This deficiency is cured by using certain local norms of the dual solution directly as weights multiplying the local residuals of the computed solution. In general, these weights have to be evaluated numerically in the course of the refinement process, yielding almost optimal meshes for various kinds of error measures. This feed-back approach is developed here for primal as well as mixed FE discretisations of the fundamental problem in linear elasticity.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 21 (1998), S. 123-133 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper a new technique for a posteriori error control and adaptive mesh design is presented for finite element models in perfect plasticity. The approach is based on weighted a posteriori error estimates derived by duality arguments as proposed in Becker and Rannacher (1996) and Rannacher and Suttmeier (1997) for linear problems. The conventional strategies for mesh refinement in finite element methods are mostly based on a posteriori error estimates for the global energy norm in terms of local residuals of the computed solution. These estimates reflect the approximation properties of the trial functions by local interpolation constants while the stability property of the continuous model enters through a global coercivity constant. However, meshes generated on the basis of such global error estimates are not appropriate in computing local quantities as point values or contour integrals and in the case of nonlinear material behavior. More accurate and efficient error estimation can be achieved by using suitable weights which can be obtained numerically in the course of the refinement process from the solutions of linearized dual problems. This feed-back approach is developed here for primal-mixed finite element models in linear-elastic perfect plasticity.
    Type of Medium: Electronic Resource
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