1,545 research outputs found

    An hphp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

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    In this paper we develop an hphp-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an hphp-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hphp-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.Comment: arXiv admin note: text overlap with arXiv:1408.522

    A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

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    In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this system exhibit boundary layers at 0. A numerical method composed of an upwind finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical examples are provided in support of the theory

    Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations

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    In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples

    A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE

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    Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is based on a model reduction approach that does not need the system to be explicitly stated in singularly perturbed form. We present examples that highlight the advantages and disadvantages of the method
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