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A Tamilselvan - One of the best experts on this subject based on the ideXlab platform.

  • Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers
    Ain Shams Engineering Journal, 2016
    Co-Authors: N Geetha, A Tamilselvan
    Abstract:

    Abstract In this paper, a numerical method based on Shishkin Mesh for a singularly perturbed fourth order differential equation with a turning point exhibiting boundary layers is presented. In this method the problem is transformed into a weakly coupled system of two second order equations, one without the Parameter e and the other with the Parameter e multiplying the highest derivative with suitable boundary conditions. We apply classical finite difference scheme on an appropriate piecewise uniform (Shishkin) Mesh. Parameter uniform error bounds for the numerical solution are established. Numerical results are provided to illustrate the theoretical results.

N Geetha - One of the best experts on this subject based on the ideXlab platform.

  • Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers
    Ain Shams Engineering Journal, 2016
    Co-Authors: N Geetha, A Tamilselvan
    Abstract:

    Abstract In this paper, a numerical method based on Shishkin Mesh for a singularly perturbed fourth order differential equation with a turning point exhibiting boundary layers is presented. In this method the problem is transformed into a weakly coupled system of two second order equations, one without the Parameter e and the other with the Parameter e multiplying the highest derivative with suitable boundary conditions. We apply classical finite difference scheme on an appropriate piecewise uniform (Shishkin) Mesh. Parameter uniform error bounds for the numerical solution are established. Numerical results are provided to illustrate the theoretical results.

Norbert Heuer - One of the best experts on this subject based on the ideXlab platform.

  • The hp-BEM with quasi-uniform Meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis
    Applied Numerical Mathematics, 2010
    Co-Authors: Alexei Bespalov, Norbert Heuer
    Abstract:

    This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart-Thomas elements on a sequence of quasi-uniform Meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, and based upon the known quasi-optimal convergence, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the Mesh Parameter h and the polynomial degree p.

  • The hp-BEM with quasi-uniform Meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis
    arXiv: Numerical Analysis, 2009
    Co-Authors: Alexei Bespalov, Norbert Heuer
    Abstract:

    This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart-Thomas elements on a sequence of quasi-uniform Meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the Mesh Parameter h and the polynomial degree p.

Alexei Bespalov - One of the best experts on this subject based on the ideXlab platform.

  • The hp-BEM with quasi-uniform Meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis
    Applied Numerical Mathematics, 2010
    Co-Authors: Alexei Bespalov, Norbert Heuer
    Abstract:

    This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart-Thomas elements on a sequence of quasi-uniform Meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, and based upon the known quasi-optimal convergence, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the Mesh Parameter h and the polynomial degree p.

  • The hp-BEM with quasi-uniform Meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis
    arXiv: Numerical Analysis, 2009
    Co-Authors: Alexei Bespalov, Norbert Heuer
    Abstract:

    This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart-Thomas elements on a sequence of quasi-uniform Meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the Mesh Parameter h and the polynomial degree p.

Julio D. Rossi - One of the best experts on this subject based on the ideXlab platform.

  • Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions
    Discrete & Continuous Dynamical Systems - B, 2002
    Co-Authors: Gabriel Acosta, Pablo Groisman, Julián Fernández Bonder, Julio D. Rossi
    Abstract:

    In this paper we study the asymptotic behavior of a semidiscrete numerical approximation for the heat equation, $u_t = \Delta u$, in a bounded smooth domain with a nonlinear flux boundary condition, $(\partial u)/(\partial\eta)= u^p$. We focus in the behavior of blowing up solutions. We prove that every numerical solution blows up in finite time if and only if $p > 1$ and that the numerical blow-up time converges to the continuous one as the Mesh Parameter goes to zero. Also we show that the blow-up rate for the numerical scheme is different from the continuous one. Nevertheless we find that the blow-up set for the numerical approximations is contained in a small neighborhood of the blow-up set of the continuous problem when the Mesh Parameter is small enough.

  • A symptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
    Journal of Computational and Applied Mathematics, 2001
    Co-Authors: Pablo Groisman, Julio D. Rossi
    Abstract:

    Abstract In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for u t = u xx + u p in a bounded interval, (0,1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical approximations and prove that it is contained in a neighbourhood of the blow-up set of the continuous problem when the Mesh Parameter is small enough.