A COMPARATIVE AND ILLUSTRATIVE STUDY FOR SOLVING SINGULARLY PERTURBED PROBLEMS WITH TWO PARAMETERS

A COMPARATIVE AND ILLUSTRATIVE STUDY FOR SOLVING SINGULARLY PERTURBED PROBLEMS WITH TWO PARAMETERS

S. Cengizci, Ö. Uğur

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Abstract

This computational study concerns approximate solutions of singularly perturbed one-dimensional boundary-value problems having perturbed convection and diffusion terms. Such kinds of problems take di erent stands depending on the perturbation parameters. Typically, when the problem is convection-dominated, classical discretization methods su er from numerical instability issues. Therefore, standard methods require special treatment in convection dominance. To this end, in this work, the standard Galerkin  nite element method (GFEM) is stabilized with the streamlineupwind/ Petrov{Galerkin (SUPG) formulation. Beyond that, an asymptotic approach, called the successive complementary expansion method (SCEM), is also proposed. Two test examples are provided to evaluate and compare the proposed methods' performances for various values of the convection and di usion parameters.

Keywords

Asymptotic expansion,  nite elements, singularly perturbed, stabilization, two parameters.