POINTWISE PERFORMANCE OF FINITE-ELEMENT METHOD IN THE CASE OF BOUNDARY-LAYER PROBLEMS

The convergence characteristics of h- and p-extensions of the finite e lement method in the case of singluarly perturbed boundary value probl ems 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 lar ge 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.