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  • 1
    Electronic Resource
    Electronic Resource
    Evolution, games theory and polyhedra (1987)
    Springer
    Journal of mathematical biology 25 (1987), S. 393-409 
    Details
    ISSN: 1432-1416
    Keywords: Evolution ; Evolutionary stable states ; Games theory ; Linear programming ; Convex polyhedra ; Linear complementarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of finding an Evolutionary Stable Strategy (ESS) for an animal species is defined. It is shown how such strategies are a subset of the equilibrium solutions for a particular non-zero sum game. These equilibrium solutions are then shown to arise from the vertices of a particular convex polyhedron. A method of finding these equilibrium solutions through the vertices and then the ESS solutions is given. This is illustrated by a number of numerical examples taken from the literature. Finally an alternative approach based on solving a Linear Complementarity Problem is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277164
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  • 2
    Electronic Resource
    Electronic Resource
    Harvesting under density-dependent mortality and fecundity (1988)
    Springer
    Journal of mathematical biology 26 (1988), S. 193-197 
    Details
    ISSN: 1432-1416
    Keywords: Optimisation ; Leslie matrix ; Equilibrium ; Linear programming ; Nonlinear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of optimal harvesting in equilibrium is considered in a Leslie matrix model in which both mortality and fecundity in all age-classes may be density-dependent. The conclusion is that the optimal strategy is of the two-age-class type, in common with results obtained previously for simpler models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277732
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  • 3
    Electronic Resource
    Electronic Resource
    Solving large nonlinear systems of equations by an adaptive condensation process (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 633-653 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; 65H15 ; 65K10 ; 65N20 ; 65N30 ; CR: G1.5
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present an algorithm which efficiently solves large nonlinear systems of the form $$Au = F(u), u \in \mathbb{R}^n $$ whenever an (iterative) solver “A −1” for the symmetric positive definite matrixA is available andF'(u) is symmetric. Such problems arise from the discretization of nonlinear elliptic partial differential equations. By means of an adaptive decomposition process we split the original system into a low dimensional system — to be treated by any sophisticated solver — and a remaining high-dimensional system, which can easily be solved by fixed point iteration. Specifically we choose a Newton-type trust region algorithm for the treatment of the small system. We show global convergence under natural assumptions on the nonlinearity. The convergence results typical for trust-region algorithms carry over to the full iteration process. The only large systems to be solved are linear ones with the fixed matrixA. Thus existing software for positive definite sparse linear systems can be used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398377
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  • 4
    Electronic Resource
    Electronic Resource
    Finite element approximation of viscoelastic progressively incompressible flows (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 43-66 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K19 ; 65N30 ; 73F05 ; 76A05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary To avoid any numerical locking in the finite element approximation of viscoelastic flow problems, we propose a three-field approximation of this problem. This approximation, which involves velocities, stresses, and pressures is proved to converge for all times. In the proof, we also obtain convergence results for the three-fields finite element approximation of incompressible elasticity problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395777
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  • 5
    Electronic Resource
    Electronic Resource
    A convergent finite element formulation for transonic flow (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 425-447 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35A40 ; 35L67 ; 35M05 ; 65L60 ; 65N30 ; 76H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A finite element formulation for the full potential equation in the case of two-dimensional transonic flow is presented. The formulation is based on an optimal control approach developed by Glowinski and Pironneau. The solution of the full potential equation is obtained by a minimization problem. Using a new compactness result it is possible to prove convergence for the solutions of the minimization problem. The a priori assumption of existence and uniqueness of a weak solution of the full potential equation satisfying an entropy condition implies that the limit function must be the solution. It is possible to extend the convergence result to the case of three-dimensional transonic potential flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396647
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  • 6
    Electronic Resource
    Electronic Resource
    Fourier-Chebyshev pseudospectral method for two-dimensional vorticity equation (1993)
    Springer
    Numerische Mathematik 66 (1993), S. 329-346 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 76D99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Fourier-Chebyshev pseudospectral scheme is proposed for two-dimensional unsteady vorticity equation. The generalized stability and convergence are proved strictly. The numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385701
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    The hierarchical basis multigrid method for convection-diffusion equations (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 7-37 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We make a theoretical study of the application of a standard hierarchical basis multigrid iteration to the convection diffusion equation, discretized using an upwind finite element discretizations. We show behavior that in some respects is similar to the symmetric positive definite case, but in other respects is markedly different. In particular, we find the rate of convergence depends significantly on parameters which measure the strength of the upwinding, and the size of the convection term. Numerical calculations illustrating some of these effects are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385495
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  • 9
    Electronic Resource
    Electronic Resource
    Arch beam models: finite element analysis and superconvergence (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 117-143 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper studies finite element methods for a class of arch beam models. For both standard and mixed methods, existence and uniqueness results are proved, optimal rates of convergence are obtained and the superconvergence property is established. Reduced integration is shown to be an efficient method for arch beam problems and selected reduced integration is found to be identical to the mixed method. The significance of the analysis is threefold. The mixed method and the reduced integration methods converge uniformly at the optimal rate with respect to the arch thickness parameter, so they are locking free. Second, mixed method and reduced integration keep the superconvergence properties of the standard method. Finally, this is the first attempt to investigate the superconvergence of finite element methods for arch beam problems. We set up two types of superconvergence results: displacement at the nodal points and gradient at the Gauss points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385501
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  • 10
    Electronic Resource
    Electronic Resource
    Convergence rate estimate for a domain decomposition method (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 153-169 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385503
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