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Abstract A continuous interior penalty method with piecewise polynomials of degree p ≥ 2 is applied on a Shishkin mesh to solve a singularly perturbed convection–diffusion problem, whose solution has… Click to show full abstract
Abstract A continuous interior penalty method with piecewise polynomials of degree p ≥ 2 is applied on a Shishkin mesh to solve a singularly perturbed convection–diffusion problem, whose solution has a single boundary layer. This method is analyzed by means of a series of integral identities developed for the convection terms. Then we prove a supercloseness bound of order 5/2 for a vertex-cell interpolation when p = 2 . The sharpness of our analysis is supported by some numerical experiments. Moreover, numerical tests show supercloseness clearly for p ≥ 3 .
Journal Title: Applied Numerical Mathematics
Year Published: 2018
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