Abstract
The paper deals with a numerical analysis of the incomplete interior penalty Galerkin (IIPG) method applied to one dimensional Poisson problem. Based on a particular choice of the interior penalty parameter σ (order of O(h −1)), we derive the optimal error estimate in the L 2-norm for odd degrees of polynomial approximation for locally quasi-uniform meshes. Moreover, we show that only the mentioned choice of the penalty parameter leads to optimal orders of convergence. Finally, presented numerical experiments verify the theoretical results.
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This work is a part of the research projects MSM 0021620839 of the Ministry of Education of the Czech Republic.
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Dolejší, V., Havle, O. The L 2-Optimality of the IIPG Method for Odd Degrees of Polynomial Approximation in 1D. J Sci Comput 42, 122 (2010). https://doi.org/10.1007/s10915-009-9319-8
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DOI: https://doi.org/10.1007/s10915-009-9319-8