The convergence characteristics of h- and p- extensions of the finite element method in the case of singularly perturbed boundary value problems are presented. For this purpose, two model problems are considered: i) a reaction-diffusion problem with large Thiele modulus; and ii) a convection-diffusion problem with large Peclet number. Based on a large number of numerical studies, it is concluded that p-extension leads to superior performance due to significantly faster convergence rates coupled with convenience in modeling.
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2.
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Woo, K.-S., and P.K. Basu, "Analysis of Singular Cylindrical Shells by p-Version of F.E.M," International Journal of Solids and Structures, vol. 25, No.2,1989, pp. 151-165.
