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  • 1
    Electronic Resource
    Electronic Resource
    Approximation in the finite element method (1972)
    Springer
    Numerische Mathematik 19 (1972), S. 81-98 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The rate of convergence of the finite element method depends on the order to which the solutionu can be approximated by the trial space of piecewise polynomials. We attempt to unify the many published estimates, by proving that if the trial space is complete through polynomials of degreek−1, then it contains a functionv h such that |u−v h | s ≦ch k−s|u| k . The derivatives of orders andk are measured either in the maximum norm or in the mean-square norm, and the estimate can be made local: the error in a given element depends on the diameterh i of that element. The proof applies to domains Ω in any number of dimensions, and employs a uniformity assumption which avoids degenerate element shapes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395933
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Approximation by translates of refinable functions (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 75-94 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65D15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The functions $f_1(x), \dots, f_r(x)$ are refinable if they are combinations of the rescaled and translated functions $f_i(2x-k)$ . This is very common in scientific computing on a regular mesh. The space $V_0$ of approximating functions with meshwidth $h=1$ is a subspace of $V_1$ with meshwidth $h=1/2$ . These refinable spaces have refinable basis functions. The accuracy of the computations depends on $p$ , the order of approximation, which is determined by the degree of polynomials $1, x, \dots, x^{p-1}$ that lie in $V_0$ . Most refinable functions (such as scaling functions in the theory of wavelets) have no simple formulas. The functions $f_i(x)$ are known only through the coefficients $c_k$ in the refinement equation – scalars in the traditional case, $r \times r$ matrices for multiwavelets. The scalar "sum rules" that determine $p$ are well known. We find the conditions on the matrices $c_k$ that yield approximation of order $p$ from $V_0$ . These are equivalent to the Strang–Fix conditions on the Fourier transforms $\hat f_i(\omega)$ , but for refinable functions they can be explicitly verified from the $c_k$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050185
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Accurate partial difference methods (1964)
    Springer
    Numerische Mathematik 6 (1964), S. 37-46 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386051
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Inverse problems and derivatives of determinants (1991)
    Springer
    Archive for rational mechanics and analysis 114 (1991), S. 255-265 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00385971
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Functions of bounded deformation (1980)
    Springer
    Archive for rational mechanics and analysis 75 (1980), S. 7-21 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the space BD(Ω), composed of vector functions u for which all components εij=1/2(u i, j+u j, i) of the deformation tensor are bounded measures. This seems to be the correct space for the displacement field in the problems of perfect plasticity. We prove that the boundary values of every such u are integrable; indeed their trace is in L 1 (Γ)N. We show also that if a distribution u yields ɛ ij which are measures, then u must lie in L p(Ω) for p≦N/(N−1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00284617
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Accurate partial difference methods I: Linear cauchy problems (1963)
    Springer
    Archive for rational mechanics and analysis 12 (1963), S. 392-402 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281235
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  • 7
    Electronic Resource
    Electronic Resource
    On multiple characteristics and the levi-lax conditions for hyperbolicity (1969)
    Springer
    Archive for rational mechanics and analysis 33 (1969), S. 358-373 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00247694
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Dual extremum principles in finite deformation elastoplastic analysis (1989)
    Springer
    Acta applicandae mathematicae 17 (1989), S. 257-267 
    Details
    ISSN: 1572-9036
    Keywords: 73Exx ; 73Gxx ; Elastoplasticity ; variational principles ; convex analysis ; finite deformation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dual extremum principles are established in this paper for the variational boundary-value problem of elasto-perfect plasticity with large deformation. There exists a duality gap between the primal and dual variational problems. Our application to nonlinear limit analysis yields a pair of dual bounding theorems for the safety factor, when the gap has the right sign. It is proved that both the upper and lower bounds directly depend on the properties of the dual gap function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047073
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    The solution of nonlinear finite element equations (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1613-1626 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi-Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141104
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  • 10
    Electronic Resource
    Electronic Resource
    A homework exercise in finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110302
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    Paper (German National Licenses)
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