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  • Articles  (24)
  • AMS(MOS): 65N30  (10)
  • 05 B 35  (7)
  • 92A07  (7)
  • Springer  (24)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Hindawi
  • Institute of Electrical and Electronics Engineers
  • Molecular Diversity Preservation International
  • Springer Science + Business Media
  • 2020-2022
  • 2010-2014
  • 1985-1989  (24)
  • 1960-1964
  • 1989  (24)
  • Mathematics  (24)
  • Geography
  • Architecture, Civil Engineering, Surveying
Collection
  • Articles  (24)
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Keywords
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  • Springer  (24)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Hindawi
    • +
Years
  • 2020-2022
  • 2010-2014
  • 1985-1989  (24)
  • 1960-1964
Year
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  • Mathematics  (24)
  • Geography
  • Architecture, Civil Engineering, Surveying
  • 1
    Electronic Resource
    Electronic Resource
    Some new families of finite elements for the stokes equations (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 827-838 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We introduce a way of using the mixed finite element families of Raviart, Thomas and Nedelec [13, 14], and Brezzi et al. [5–7], for constructing stable and optimally convergent discretizations for the Stokes problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405291
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  • 2
    Electronic Resource
    Electronic Resource
    On the convergence of the Galerkin method for nonsmooth solutions of integral equations (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 295-302 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65R20 ; 45J05 ; 45L10 ; 35S99 ; 31C20 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that the stability region of the Galerkin method includes solutions not lying in the conventional energy space. Optimal order error estimates for these nonsmooth solutions are derived. The new result is compared with the classical statement by means of the basic potential problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396763
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  • 3
    Electronic Resource
    Electronic Resource
    A second order splitting method for the Cahn-Hilliard equation (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 575-590 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A semi-discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary, fourth order in space, Cahn-Hilliard equation. Optimal order error bounds are derived in various norms for an implementation which uses mass lumping. The continuous problem has an energy based Lyapunov functional. It is proved that this property holds for the discrete problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396363
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  • 4
    Electronic Resource
    Electronic Resource
    Finite element variational crimes in parabolic-elliptic problems (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 343-376 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M60 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The study of a completely discretized variational problem corresponding to a nonlinear second order parabolic-elliptic initial-boundary value problem with an initial value only inL 2 is presented. The discretization in time is done by the Euler backward method, the discretization in space by the finite element method with linear functions on triangular elements. The changes in domain are taken into account. The convergence and the unconditional stability of the method is proved under the assumption that the boundary ∂Ω is piecewise of classC 3 and the forma(v, w) has a potential and is strongly monotone and Lipschitz continuous. As a by-product the existence and uniqueness theorem is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390058
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  • 5
    Electronic Resource
    Electronic Resource
    A relaxation procedure for domain decomposition methods using finite elements (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 575-598 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present the convergence analysis of a new domain decomposition technique for finite element approximations. This technique was introduced in [11] and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent. No global preconditioner is needed in the practice, but simply single-domain finite element solvers are required. An optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated. Applications are given to both elliptic equations and incompressible Stokes equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398917
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  • 6
    Electronic Resource
    Electronic Resource
    A family of mixed finite elements for linear elasticity (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 633-666 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR:G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A family of finite elements for use in mixed formulations of linear elasticity is developed. The stresses are not required to be symmetric, but only to satisfy a weaker condition based upon Lagrange multipliers. This is based on the same formulation used in the PEERS finite element spaces. Elements for both two and three dimensional problems are given. Error analysis on these elements is done, and some superconvergence results are proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389334
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  • 7
    Electronic Resource
    Electronic Resource
    The numerical computation of compressed states of nonlinearly elastic anisotropic plates (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 93-107 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we study the numerical computation of the compressed states of nonlinearly elastic anisotropic circular plates. The singular boundary value problem giving the compressed states depend parametrically on the applied pressure at the edge of the plate. We give a finite difference approximation of this problem and derive bounds for the global error by using the techniques of Brezzi, Rappaz and Raviart for the finite dimensional approximation of nonlinear problems. Some numerical results are given for a class of materials whose constitutive functions reflect the standard Poisson ratio effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395780
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  • 8
    Electronic Resource
    Electronic Resource
    The convergence of two numerical schemes for the Navier-Stokes equations (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 33-60 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with some convergence/stability results concerning two numerical methods for solving the incompressible nonstationary Navier-Stokes equations. The algorithms are of a particular kind in what regards time discretization (more precisely, of the Peaceman-Rachford and the Strang type resp.), and have been obtained by modifying slightly the numerical treatment of the nonlinear terms in other schemes due to Glowinski et al. (1980). We first describe the full discretization of the homogeneous Dirichlet problem using a (general) external approximation of the spatial functional spaces involved (a particular and simple choice of such an approximation is the standardP 2-Lagrange finite element for the velocity field when the fluid is bidimensional). Then we establish and prove convergence and stability and make some comments on the numerical treatment of other (generally nonhomogeneous) boundary conditions. The theoretical results show that the schemes are (at least) conditionally stable and convergent, which justifies the success of Glowinski's methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395871
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  • 9
    Electronic Resource
    Electronic Resource
    Pointwise error estimates for a streamline diffusion finite element scheme (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 707-719 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Pointwise error estimates for a streamline diffusion scheme for solving a model convection-dominated singularly perturbed convection-diffusion problem are given. These estimates improve pointwise error estimates obtained by Johnson et al.[5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405198
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  • 10
    Electronic Resource
    Electronic Resource
    Extrapolation methods for spline collocation solutions of pseudodifferential equations on curves (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 385-407 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this article we consider extrapolation methods in approximating smooth linear functionals by means of collocation solutions of boundary integral equations. We are able to derive an asymptotic expansion of the error. In main applications this expansion covers arbitrary high powers of the discretization parameter if the boundary solution is smooth. The expansion gives rise to Richardson-type extrapolation schemes which require only simple postprocessing of calculated numbers. The results are applicable for example in calculating pointwise values in the space domain, when solving boundary value problems by means of integral equations. In such examples the extrapolation rapidly improves the original rate of the convergence. Numerical experiments conform our results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396612
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