1,545 research outputs found
An -Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems
In this paper we develop an -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 -version adaptive finite element
discretization (based on a robust a posteriori residual analysis), thereby
leading to a fully -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
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
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
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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