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  • Articles  (133)
  • CR: G1.8  (133)
  • Mathematics  (133)
  • 1
    Electronic Resource
    Electronic Resource
    A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 169-186 
    Details
    ISSN: 1572-9044
    Keywords: symmetric positive definite linear system ; block SSOR iteration ; preconditioner ; hierarchical basis discretization ; 65F10 ; 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of modified block SSOR preconditioners is presented for solving symmetric positive definite systems of linear equations, which arise in the hierarchical basis finite element discretizations of the second order self‐adjoint elliptic boundary value problems. This class of methods is strongly related to two level methods, standard multigrid methods, and Jacobi‐like hierarchical basis methods. The optimal relaxation factors and optimal condition numbers are estimated in detail. Theoretical analyses show that these methods are very robust, and especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018974514896
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  • 2
    Electronic Resource
    Electronic Resource
    Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 697-721 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuška paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398380
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  • 3
    Electronic Resource
    Electronic Resource
    Applications of fixed-point methods to discrete variational and quasi-variational inequalities (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 631-654 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20, 65N10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, discrete analogues of variational inequalities (V.I.) and quasi-variational inequalities (Q.V.I.), encountered in stochastic control and mathematical physics, are discussed. It is shown that those discrete V.I.'s and Q.V.I.'s can be written in the fixed point formx=Tx such that eitherT or some power ofT is a contraction. This leads to globally convergent iterative methods for the solution of discrete V.I.'s and Q.V.I.'s, which are very suitable for implementation on parallel computers with single-instruction, multiple-data architecture, particularly on massively parallel processors (M.P.P.'s).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400174
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  • 4
    Electronic Resource
    Electronic Resource
    Compactness method in the finite element theory of nonlinear elliptic problems (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 147-163 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Finite element approximation of a nonlinear elliptic pseudomonotone second-order boundary value problem in a bounded nonpolygonal domain Ω with mixed Dirichlet-Neumann boundary conditions is studied. In the discretization we approximate the domain Ω by a polygonal one, use linear conforming triangular elements and evaluate integrals by numerical quadratures. We prove the solvability of the discrete problem and on the basis of compactness properties of the corresponding operator (which is not monotone in general) we prove the convergence of approximate solutions to an exact weak solutionu∈H 1 Ω). No additional assumption on the regularity of the exact solution is needed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398687
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  • 5
    Electronic Resource
    Electronic Resource
    Extrapolation techniques for reducing the pollution effect or reentrant corners in the finite element method (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 539-564 
    Details
    ISSN: 0945-3245
    Keywords: AMS(OMS): 65N30, 65B05, 73K25 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Standard finite element schemes applied to boundary value problems on domains with reentrant corners suffer from a global loss of accuracy caused by the influence of the corner singularities. For a model situation, it is shown that this pollution effect can be completely described in terms of an asymptotic error expansion with respect to fractional powers of the mesh size parameter. This provides the basis of an extrapolation procedure which recovers the full order of accuracy for the solution as well as for the corresponding stress intensity factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400891
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  • 6
    Electronic Resource
    Electronic Resource
    Approximation by finite differences of the propagation of acoustic waves in stratified media (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 655-702 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we analyze the approximation of acoustic waves in a two layered media by a finite diffrences variational scheme. We examine in particular the approximation of the guided waves. We point out the existence of purely numerical parasitic phenomena and quantify the numerical dispersion relative to guided waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396488
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  • 7
    Electronic Resource
    Electronic Resource
    A generalization of the schwarz alternating method to an arbitrary number of subdomains (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 61-81 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 or 65J10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give a generalization of the Schwarz alternating method to an arbitrary number of subdomains. As applications, we prove that the method converges for the main second-order boundary value problems, as well as for the system of linear elasticity. For the Dirichlet problems it is proved that the method converges geometrically and some numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395872
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  • 8
    Electronic Resource
    Electronic Resource
    Discretization of the Timoshenko Beam problem by thep and theh-p versions of the finite element method (1990)
    Springer
    Numerische Mathematik 57 (1990), S. 413-420 
    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 the discretization of the Timoshenko Beam problem by thep and theh-p versions of the finite element method is considered. Optimal error estimates are established. The locking phenomenon disappears as the thickness of the beam decreases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386420
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  • 9
    Electronic Resource
    Electronic Resource
    AnL 2-error estimate for an approximation of the solution of a parabolic variational inequality (1990)
    Springer
    Numerische Mathematik 57 (1990), S. 453-471 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We estimate the order of the difference between the numerical approximation and the solution of a parabolic variational inequality. The numerical approximation is obtained using a finite element discretization in space and a finite difference discretization in time which is more general than is used in the literature. We obtain better error estimates than those given in the literature. The error estimates are compared with numerical experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386423
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  • 10
    Electronic Resource
    Electronic Resource
    A new class of variational problems arising in the modeling of elastic multi-structures (1990)
    Springer
    Numerische Mathematik 57 (1990), S. 547-560 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown howelastic multi-structures that comprise substructures of possibly different “dimensions” (three-dimensional structures, plates, rods) are modeled bycoupled, pluri-dimensional, variational problems of a new type. Following recent work by the author, H. LeDret, and R. Nzengwa, we describe here in detail one such problem, which is simultaneously posed over a threedimensional open set with a slit and a two-dimensional open set. The numerical analysis of such problems is also discussed and finally, some numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386427
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