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  • 1
    Electronic Resource
    Electronic Resource
    Finite element analysis of a holonomic elastic-plastic problem (1991)
    Springer
    Numerische Mathematik 60 (1991), S. 493-508 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A thorough analysis of the finite element method is given for a holonomic elastic-plastic problem. An inequality of the Cea's lemma type is proved, which is the basis of error estimates for various finite element solutions. Difficulty caused by a non-differentiable term in the problem can be overcome by using two convergent procedures, an iterative procedure and a regularization procedure. An a-posteriori quantitative error estimate is derived for the regularized solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385733
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence of approximations to the primal problem in plasticity under conditions of minimal regularity (2000)
    Springer
    Numerische Mathematik 87 (2000), S. 283-315 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65M60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. This work considers semi- and fully discrete approximations to the primal problem in elastoplasticity. The unknowns are displacement and internal variables, and the problem takes the form of an evolution variational inequality. Strong convergence of time-discrete, as well as spatially and fully discrete approximations, is established without making any assumptions of regularity over and above those established in the proof of well-posedness of this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110000194
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  • 3
    Electronic Resource
    Electronic Resource
    The regularization method for an obstacle problem (1994)
    Springer
    Numerische Mathematik 69 (1994), S. 155-166 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65K10, 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We give a relatively complete analysis for the regularization method, which is usually used in solving non-differentiable minimization problems. The model problem considered in the paper is an obstacle problem. In addition to the usual convergence result and a-priori error estimates, we provide a-posteriori error estimates which are highly desired for practical implementation of the regularization method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050086
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical approximations of problems in plasticity: error analysis and solution algorithms (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 4 (1997), S. 191-204 
    Details
    ISSN: 1070-5325
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The initial-boundary value problem of elastoplasticity is considered in the form of a variational inequality, with primary unknowns the displacement, plastic strain and internal variables. The well-posedness of this problem is reviewed, and results are presented for the convergence of a new fully discrete scheme, in which a non-differentiable functional characteristic of this problem is replaced by an approximate discrete function. It is shown that convergence of this approximation is at the same rate as that for approximations based on the use of the original functional, and that the scheme is stable. Some iterative solution algorithms are discussed. ©1997 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 487-508 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170702
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  • 6
    Electronic Resource
    Electronic Resource
    Quantitative error estimates for coefficient idealization in linear elliptic problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 971-987 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171206
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  • 7
    Electronic Resource
    Electronic Resource
    Minimal-energy splines: I. Plane curves with angle constraints (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 351-372 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This is the first in a series of papers on minimal-energy splines. The paper is devoted to plane minimal-energy splines with angle constraints. We first consider minimal-energy spline segments, then general minimal-energy spline curves. We formulate problems for minimal-energy spline segments and curves, prove the existence of solutions, justify the Lagrange multiplier rules, and obtain some nice properties (e.g., the infinite smoothness). Finally, we report our computational experience on minimal-energy splines.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130407
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  • 8
    Book
    Book
    Quasistatic contact problems in viscoelasticity and viscoplasticity; 30 (2002)
    Providence, RI :AMS,
    Details
    Title: Quasistatic contact problems in viscoelasticity and viscoplasticity; 30
    Author: Han, Weimin
    Contributer: Sofonea, Mircea
    Publisher: Providence, RI :AMS,
    Year of publication: 2002
    Pages: XIII, 442 S.
    Series Statement: AMS/IP studies in advanced mathematics 30
    ISBN: 0-8218-3192-5
    Type of Medium: Book
    Language: German
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  • 9
    Book
    Book
    Analysis and approximation of contact problems with adhesion or damage /; 276 (2005)
    Boca Raton :Taylor & Francis,
    Details
    Title: Analysis and approximation of contact problems with adhesion or damage /; 276
    Author: Sofonea, Mircea
    Contributer: Han, Weimin , Shillor, Meir
    Publisher: Boca Raton :Taylor & Francis,
    Year of publication: 2005
    Pages: XVIII, 220 S.
    Series Statement: Monographs and textbooks in pure and applied mathematics 276
    ISBN: 1-584-88585-8
    Type of Medium: Book
    Language: English
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  • 10
    Book
    Book
    Theoretical numerical analysis /; 39 (2009)
    New York, NY :Springer,
    Details
    Title: Theoretical numerical analysis /; 39
    Author: Atkinson, Kendall E.
    Contributer: Han, Weimin
    Edition: 3. ed.
    Publisher: New York, NY :Springer,
    Year of publication: 2009
    Pages: XVI, 625 S. : , graph. Darst. ; , 235 mm x 155 mm
    Series Statement: Texts in applied mathematics 39
    ISBN: 978-1-441-90457-7 , 978-1-4419-0458-4
    Type of Medium: Book
    Language: English
    URL: http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1181.47078
    URL: 01 Inhaltstext
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