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  • Articles  (146)
  • 2010-2014  (146)
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  • Articles  (146)
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  • 1
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    A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-12-21
    Description: Our aim in this paper is to study the interaction between surface and subsurface flows. The model considered is a system coupling Navier–Stokes and Darcy equations. We make use of a discontinuous Galerkin finite element method for the discretisation of this problem. Then we develop a posteriori error analysis for the resulting discrete problem. Numerical experimentations confirm our analytical results.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 2
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    On the quality of complementary bounds for eigenvalues (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-12-10
    Description: A concrete formulation of the Lehmann–Maehly–Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determined in terms of how well the trial spaces capture the spectral subspace of the operator. Optimality of the choice of a shift parameter which is intrinsic to the method is also examined. The main theoretical findings are illustrated by means of a few numerical experiments involving one-dimensional Schrödinger operators.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 3
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    Abstract multiscale-hybrid-mixed methods (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-12-05
    Description: In an abstract setting, we investigate the basic ideas behind the Multiscale Hybrid Mixed (MHM) method, a Domain Decomposition scheme designed to solve multiscale partial differential equations (PDEs) in parallel. As originally proposed, the MHM method starting point is a primal hybrid formulation, which is then manipulated to result in an efficient method that is based on local independent PDEs and a global problem that is posed on the skeleton of the finite element mesh. Recasting the MHM method in a more general framework, we investigate some conditions that yield a well-posed method. We apply the general ideas to different formulations, and, in particular, come up with an interesting and fruitful connection between the Multiscale Finite Element Method and a dual hybrid method. Finally, we propose a method that combines the main ideas of the Discontinuous Enrichment Method and the MHM method.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 4
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    Jacobi spectral Galerkin methods for fractional integro-differential equations (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-11-21
    Description: We propose general spectral and pseudo-spectral Jacobi–Galerkin methods for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide rigorous error analysis for spectral and pseudo-spectral Jacobi–Galerkin methods, which show that the errors of the approximate solution decay exponentially in \(L^\infty \) norm and weighted \(L^2\) -norm. The numerical examples are given to illustrate the theoretical results.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 5
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    Quadratic mixed finite element approximations of the Monge–Ampère equation in 2D (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-11-11
    Description: We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge–Ampère equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar variable and the Hessian matrix.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 6
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    Normality conditions for the matrix operator $$X \rightarrow AX + X^{*}B$$ X → A X + X (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-10-28
    Description: The operator defined by the left-hand side of the matrix equation $$\begin{aligned} AX + X^{*} B = C \end{aligned}$$ is not linear in the space of complex matrices \(X\) . However, it becomes a linear operator if every matrix \(X\) is replaced by the pair of real matrices of the same size, namely, by its real and imaginary parts. Introducing an appropriate scalar product in the resulting real space, we find necessary and sufficient conditions for this operator to be normal.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 7
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    Near-best $$C^2$$ C 2 quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-10-10
    Description: In this paper, we present new quasi-interpolating spline schemes defined on three-dimensional bounded domains, based on trivariate \(C^2\) quartic box splines on type-6 tetrahedral partitions and with approximation order four. Such methods can be used for the reconstruction of gridded volume data. More precisely, we propose near-best quasi-interpolants, i.e. with coefficient functionals obtained by imposing the exactness of the quasi-interpolants on the space of polynomials of total degree three and minimizing an upper bound for their infinity norm. In case of bounded domains the main problem consists in the construction of the coefficient functionals associated with boundary generators (i.e. generators with supports not completely inside the domain), so that the functionals involve data points inside or on the boundary of the domain. We give norm and error estimates and we present some numerical tests, illustrating the approximation properties of the proposed quasi-interpolants, and comparisons with other known spline methods. Some applications with real world volume data are also provided.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 8
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    Strong convergence and stability of backward Euler–Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-08-14
    Description: In the paper, our main aim is to investigate the strong convergence and almost surely exponential stability of an implicit numerical approximation under one-sided Lipschitz condition and polynomial growth condition on the drift coefficient, and polynomial growth condition on the diffusion coefficient. After providing almost surely exponential stability and moment boundedness for the exact solution, we show that an appropriate implicit numerical method preserves boundedness of moments, and the numerical approximation converges strongly to the true solution. Moreover, we prove that the backward Euler–Maruyama approximation can share almost surely exponential stability of the exact solution for sufficiently small step size.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 9
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    Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-08-07
    Description: This work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 10
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    Computational evaluation of multi-iterative approaches for solving graph-structured large linear systems (2014)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2014-07-30
    Description: We analyse the practical efficiency of multi-iterative techniques for the numerical solution of graph-structured large linear systems. In particular we evaluate the effectiveness of several combinations of coarser-grid operators which preserve the graph structure of the projected matrix at the inner levels and smoothers. We also discuss and evaluate some possible strategies (inverse projection and dense projection) to connect coarser-grid operators and graph-based preconditioners. Our results show that an appropriate choice of adaptive projectors and tree-based preconditioned conjugate gradient methods result in highly effective and robust approaches, that are capable to efficiently solve large-scale, difficult systems, for which the known iterative solvers alone can be rather slow.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
    Published by Springer
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